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Ncfm derivatives module pdf

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Distribution of weights of the Derivatives Market (Dealers) Module for NCFM test (s) for announcements pertaining to revisions/updations in NCFM modules or . All content included in this book, such as text, graphics, logos, images, data compilation etc. are the property of NSE. This book or any part thereof should not be. NCFM's workbook titled Options Trading (Advanced) module gets into some of the quantitative aspects of Download as PDF, TXT or read online from Scribd.


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Q What are the instruments traded in the derivatives industry, and what Q1. 12 Worldwide, what kinds of derivatives are seen on the equity market? 7. Derivatives Market (Dealers) Module (DMDM). ➢ Introduction to Derivatives. Types of Derivative Contracts, History of Financial Derivatives Markets,. Participants. Derivatives are securities under the SC(R)A and hence the trading of derivatives In the class of equity derivatives the world over, futures and options on stock.

Interest is payable semi-annual. For example, the market lot contract multiplier for Futures on Nifty Index is There is a reason for this. Final Settlement When CDS-sellers defaulted. This will give him the right, but not an obligation to do the swap after 2 years. Since each T-Bill has a face value of Rs.

The index on which futures and options contracts are permitted shall be required to comply with the eligibility criteria on a continuous basis. In such instances. On such confirmation. On such confirmation the Exchange may approve such order.

NSCCL introduces itself as a party between the two independent parties. The margins are monitored on-line on intra-day basis. In respect of orders which have come under quantity freeze. In respect of orders which have come under price freeze. While a trade may be executed based on quotes of two independent parties in NEAT.

These are collected from both parties to the futures contract. The following types of margins are prevalent: This ensures that even if one of the counter-parties does not meet its obligation.

NSCCL will settle the obligation to the other counter-party. It is a highly sophisticated. In all other cases. The initial and exposure margin is payable upfront by Clearing Members. Fixed Deposit Receipts and approved securities. Margins can be paid by members in the form of Cash. Purchase of a futures contract for one month. The standard deviation of daily logarithmic returns of prices in the underlying stock in the cash market in the last six months is computed on a rolling and monthly basis at the end of each month.

On stock futures. In case of calendar spread positions in futures contract. The Clearing Members who have suffered a loss are required to pay the mark-to-market loss amount to NSCCL which is passed on to the members who have made a profit. Bank Guarantee.

Clearing members who are clearing and settling for other trading members can specify in the NEAT system. The calendar spread position is granted calendar spread treatment till the expiry of the near month contract.

This is known as daily mark-to-market settlement. Such limits can be set up by the clearing member. The option once exercised shall remain irrevocable during that quarter. If the futures are available at a price lower than Rs. Reliance Futures with expiry on March Open positions in futures contracts cease to exist after their expiration day.

The calculations are refined in the next section. The total acquisition cost would thus be Rs. On the same day. If an investor is bullish on Reliance. The final settlement of the futures contracts is similar to the daily settlement process except for the method of computation of final settlement price. Assume no margin payments If the investor were to buy in the cash market.

The option can be exercised once in a quarter Jan-March. The interest cost would be Rs. An investor holding the underlying share will receive the dividend. Drawing on the calculations in Chapter 1. But the holder of Reliance Futures will not be entitled to the dividend. The risk-free rate of interest that equates the cash price to the futures price is the cost of carry.

Cost of carry on continuous basis is 6. The no-arbitrage futures price will be calculated as follows: This will raise the Nifty spot or pull down Nifty futures. Since various companies will pay a dividend at different points of time. This dividend rate is directly subtracted from the cost of carry. If Nifty Futures is trading higher. The price for March 28 Nifty Futures can be calculated as: They will buy Nifty basket in spot and sell Nifty futures.

It is an arbitrage transaction. Arbitragers do not want to take an exposure. Profitability will be lower to the extent of interest cost on the margin payments. Let us now examine the role of arbitrager in detail. If the shares were trading at a price higher than Rs. The role of arbitrager in restoring equilibrium was also discussed. Reliance Shares Rs.

The profit does not depend on the price of Reliance shares on March March Sell Reliance Shares in the Cash Market say. The net arbitrage profit would remain the same.

This is the essence of arbitrage — future change in price of the underlying does not affect the net profit or loss. The investor would do the following trades: March 8: A point to note is that in these calculations. Buy Reliance Shares in the Cash Market say. Closer to maturity of the contract. Figure 2. Receive interest income of Rs.

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On maturity of the futures contract. The graph depicts the convergence along a straight line. This is the normal position for equity futures that do not involve a dividend. In such situations. This is more common with commodity futures rather than financial futures. Such a relative price position is called contango.

At times. F is the theoretical price of a commodity future S0 is the spot price of the underlying commodity PV SC is the present value of storage costs over the duration of the contract PV CY is the present value of the convenience yield over the duration of the contract. The position yielded a return in the form of dividend besides capital gain. Investment in commodities like gold and oil entail another element of cost viz.

Adjustment for dividend while valuing equity futures has already been discussed. These elements are part of the calculation of price of commodity futures. Continuously Compounded basis: Futures on Stock X. What trade should he do and how much will he earn in the process. Even if not straight. This direct relationship between spot and futures contracts is depicted in Figure 3.

Chapter 3 Investment with Equity Futures 3. Figure 3. On the other hand. The relationship can be seen in the payoff matrix shown in Figure 3. But since the seller has short-sold the contract. When the underlying grows in value. The relationship can be seen in payoff matrix shown in Figure 3. Based on its beta. How many Nifty futures to sell. The revised contract value would be 6.

The beta value of 0. Suppose the beta of Infosys is 0. The notional value of each Nifty Futures contract is 6. The value of Nifty Futures to sell would be Rs. This would translate to a share price of Rs. This is a company he is bullish about. He can hedge himself against a general decline in the market. The gain on Infosys shares purchased would have been: He is however concerned that if the general market goes down.

How much of the risk is eliminated by selling Nifty futures? The answer lies in the R-square value. If the Nifty is at 6. Selling Nifty Futures to hedge against purchase of Infosys shares is not a perfect hedge selling Infosys Stock Futures would be more perfect.

For example: Y stands for returns in the Futures contracts and X stands for returns based on the Spot prices. Infosys Futures are a perfect hedge for Infosys shares.

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R-square is 1 i. To illustrate the point. In reality. It arises because Nifty is not a perfect hedge for shares of Infosys. Selling 28 Nifty Futures contracts brought down the portfolio beta from 0. The hedger has no option but to hedge for 3 months. If the portfolio had only this one share. Suppose he wanted to bring the portfolio beta to 0. By selling the requisite Nifty futures. The same process will be repeated at the end of each quarter.

In this manner. In order to bring down the portfolio beta to 0. Before getting into a position. At the end of 3 months. In the Infosys example. Its beta is 0. How will he hedge his position? NSE specifies a list of securities that are eligible for delivery. Offering futures on each individual debt security is not practical. Interest rate options are not permitted in India yet. Chapter 4 Interest Rate Futures Just as risks in the equity market can be varied or hedged through equity futures.

This list is prepared based on the following criteria: As market yields go up. Trading hours are 9 am to 5 pm from Monday to Friday. In any case. We know that an investor can protect himself from a decline in equity prices by selling equity futures.

For instance. Table 4. NSE also announces a conversion factor for each eligible security for each contract. The conversion factor is equal to the price of the deliverable security per rupee of principal on the first calendar day of the delivery month.

When a party purchases a bond in the market. If the buyer holds the bond long enough. The concept is illustrated in Table 4. A party purchasing the bond on July 15 will pay the clean price and accrued interest for the period July 1 to July The issuer will pay the interest to the holder of the bonds on the interest payment date. This is compensation for the seller for having held the bonds for the period since the last interest payment date.

Out of these. Quantity freeze limit is 1. September and December. In cases where the positions are open at end of last trading day and no intention to deliver has been received.

Daily MTM margin is calculated based on daily settlement price. Once the positions are intended for delivery and allocation has been done.

These are levied on both buyer and seller. That is also the last day for sellers to intimate their intention regarding delivery of the underlying by 6 pm. The delivery day is the last business day of the contract expiry month. The last trading day for a contract is 2 business days prior to settlement delivery date. But the underlying is a T-Bill that will mature 91 days later. The summation of the two periods. Suppose the settlement date is April December In case the last Wednesday of the month is a designated holiday.

The T-Bill will be valued in the money market at Rs. May While the futures contract would expire on a Wednesday. The period of 13 days from April June Quantity freeze limit is 7. This is the quote price.

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This is the valuation price. Since each T-Bill has a face value of Rs. The near month futures contract will expire on April September Final settlement on expiry of contracts is through physical delivery of securities. They expire at 1 pm on the last Wednesday of the concerned month.

Money market yield is Rs. Suppose the yield was 4. The buyer of the future has made a loss of Rs. The buyer of the futures contract has made a MTM profit of Rs. The final settlement price is worked out on the basis of weighted average discount yield obtained from weekly 91 Day T-Bill auction of RBI. It is subject to minimum of 0. Since yield has gone up.

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The weighted average is calculated on the basis of: All T-Bill futures are cash settled in this manner. In the absence of adequate trades. On the contract of 2. Since each contract represents 2. At this price. Final settlement is done one day after expiry of the contract. Suppose futures contract was executed at valuation price of Rs. The final settlement price would be Rs. For the daily MTM margin. A 3-month option on that stock has exercise price of Rs.

What would be its price as per Black Scholes model. Excel function NORM. C stands for Call option S0 is the current price of the stock i. True is used to arrive at the value. DIST X. DIST 2. The total acquisition cost of a share on exercise of call would be Rs. DIST Example 5. Exercise of a call option would entail an immediate payment of exercise price. This is a significant reason why an option may not be exercised. It would be better to sell the call option with a gain if it is in the money.

This will be lost. The benefit of keeping an option position open is the insurance it offers to the portfolio. Only if a large dividend is expected on the stock during the life of an option. The position regarding exercise varies between call and put options.

In such cases. Exercise of a put option leads to immediate receipt of money.

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In this situation again. Black Scholes can be applied even for American call options. Black Scholes can be applied. If the Black Scholes value turns out to be lower than the intrinsic value. This makes the put more valuable. After a dividend is paid. What would be its price if it is an European Call? A 1-month option on that stock has exercise price of Rs. What would be its price if it is an European Put?

Delta varies with the stock price. Chapter 6 Option Greeks Knowledge of options in the Black Scholes framework is incomplete without understanding the Greeks. Example 6. A stock. The relation between delta and stock price for this option is shown in Figure 6.

Substituting the values in the above formula. The Y-axis on the left of the graph shows the value of call delta at different values of the stock price. The stock is trading at Rs. The secondary Y axis on the right of the graph in Figure 6. The put delta has the same shape as the call delta. Figure 6. The graph looks like the normal distribution bell-shaped curve. The movement in gamma of the option mentioned in Example 6. Gamma is high when the option is at the money.

The longer extension on the right side implies that for the same difference between stock price and exercise price. As seen Figure 6. It is an indicater of the benefit for the option holder and problem for the option seller on account of fluctuations in the stock price. Gamma is the same for both call and put options. Thetais usually negative. Theta is the sensitivity of the value of the option with respect to change in time to maturity assuming everything else remains the same.

The value is — 0. Per day value of Theta which is more meaningful is calculated by dividing by Per day value of Theta is — 0. Call on a dividend paying stock can have a positive theta. Change in value of Theta of both call and put options as the stock price changes can be seen in Figure 6. The call and put options have the same Vega. Vega is maximum around the exercise price. The change in Vega for different values of the stock price for the option in Example 6. The same formulae can be used even in the case of a dividend-paying stock.

Quantity freeze comes into effect if the order is for more than Contracts are traded on a 12 month trading cycle. Daily settlement price is based on weighted average price in last half hour of trading. Speculaters wish to benefit from expected changes in the exchange rates. Currency futures are available on four currency pairs viz. As in the case of equity and debt. The final settlement price is the RBI reference rate.

Most international transactions entail an exposure to a foreign currency. Initial margin is based on SPAN. Each contract represents 1. Final settlement is on the last business day. They expire at 12 noon. Theoretical daily settlement price is computed for unexpired futures contracts. Different calendar spread margins are prescribed in rupees for various currencies and contract periods.

Quantity freeze would be applicable beyond Foreign risk free interest rate is the relevant LIBOR rate or such other rate as may be specified by the Clearing Corporation from time to time. He needs to convert it to INR in a year.

The value of a 1-year future on the USD is calculated as: He can do the conversion right away. If futures were being traded in the market at an underlying exchange rate of Rs. There is a lack of transparency in offering these rates. Instead of currency futures.

This is the same as the immediate conversion option minor difference being on account of rounding off. X will not be able to deliver the USD 1. X can enter into a forward rate agreement with the bank to sell USD at the end of 1 year at a rate that is decided today. The benefit of this approach for X is: He is not constrained by the USD 1.

USD 1. Initial margin would need to be paid. X would be subject to margin payments. But since the contracts are available in multiples of USD 1.

The USD 1. Speculaters in the market ensure that futures prices remain closer to the no-arbitrage price. He will sell it to his bank at the spot rate prevailing at the end of 1 year. At the futures exchange rate. In India. The premium is quoted in INR.

The last trading day is two working days prior to the last business day of the expiry month. Each contract unit represents 1.

Strikes are available at intervals of Rs. All in-the-money open long contracts are automatically exercised at the final settlement price and assigned on a random basis to the open short positions of the same strike and series. In a forward rate agreement however. All contracts are cash settled in rupees. X will get the benefit of this favourable movement in exchange rates only at the end of the forward period. Currency futures. June and September Initial margin.

Final settlement day is the last business day of the expiry month. X can keep receiving margin payments on the currency futures he has sold. Final settlement price is the RBI reference rate on the date of expiry of the contract.

Quantity freeze kicks in for orders above C stands for Call option S0is the current price of the foreign currency i. A 3-month option on USD has exercise price of Rs. If the USD were to strengthen considerably. DIST 0. X can choose to let the option lapse. X was committed to an exchange rate. He would have had to pay an option premium for buying the put option contract which would have given him the right to sell USD 1.

X cannot benefit from that movement. Similar problems are included in the Examination] 7. The extra money that he will earn by selling the USD at a higher rate would more The extra money thus earned on the put option.

Y can let the call option lapse. The benefit that it will have of buying USD at this low price will more than cover for the option premium paid. It will need to pay an option premium. As in the case of futures. The gain on that will cover Y for the higher price at which it will buy the USD from its bank in the cash market.

On continuously compounded basis. What should be the price for a 6-month currency futures contract? In such trades. Suppose Party A is worried about its 2-year loan of Rs. Often a bank finds two parties with divergent views about the market interest rates. The payments may cover only interest..

So the two parties will know each other when the bank brokers the swap. The bank performs either of two roles: This is the reason parties explore exchange traded futures and options. Since swaps are OTC products. As broker. Chapter 8 Swaps Swaps are contracts where the two parties commit to exchange two different streams of payments. The bank is however exposed to credit risk from both parties. These are not traded in a stock exchange.

If interest rates were to go up, it will have to pay higher interest to its lender. On the other hand, Party B is worried that interest rates may fall, and it will earn less on its deposits. Party A and Party B can do an interest rate swap.

While the swap may be direct between Party A and Party B, it is understood better if we bring in a 3rd party viz. The bank that brings Party A and Party B together may be a 4th party. The position of the 3 parties is shown in Figure 8.

Figure 8. The actual cash flows of the parties are shown in Table 8. On the Rs. A few points to note: The swap is a separate transaction between Party A and Party B. The parties avoid multiple payments by netting. An interest rate swap has only interest payments. Since no principal is paid, the cash flows are not like a normal coupon bearing bond. However, by assuming a receipt and payment on maturity, the cash flows can be made to look like a coupon bearing bond.

Receipt and payment of the same amount on maturity will net each other. Therefore, it does not affect the economics of the swap in any way, but aids valuing the swap as a bond.

If Party A were to pay Rs. Receipt of Rs. It has effectively sold a fixed rate bond and purchased a floating rate bond. The value of the Swap for Party A can be defined as: The two bonds can be valued on yield to maturity YTM basis like any debt security.

The swap is normally initiated at prevailing interest rates. Therefore, initially, the value of When yields go up, fixed rate instruments lose value.

Therefore, Valuation. The value of the swap for Party B is Valuation. When yields go down, fixed rate instruments gain value. There is a reason for this. If MIBOR were to change, the floating rate instrument will in any case pay the changed rate for the next interest cycle. Therefore, it will be at par on the next interest payment date. Suppose that on Jan 1, , the 1-year yield is at 8.

Thus, the swap is beneficial to Party A. How much is that benefit? The calculation is shown in Table 8. Table 8. Party B has lost out on the Swap. The FRA approach uses different discount rates for each cash flow.. When the swap is initiated. On maturity. FRA is an agreement to lend money on a future date at an interest rate that is decided today. This translates to a return of Party D agrees to pay Party R. Suppose Party D and Party R. In the earlier example.

What then. This is equivalent to 8. In return. The bond pricing example used a single 8. This more complex approach is often used for valuing exotic swaps. Party D has done the reverse viz.

As the put option goes deeper in the money stock price significantly below Rs. When the put option goes deeper out of the money stock price significantly above Rs. When the stock price is closer to the exercise price, the delta of the put option is closer to 0. Gamma measures the rate of change of delta as the stock price changes. It is an indicater of the benefit for the option holder and problem for the option seller on account of fluctuations in the stock price. As seen Figure 6.

Therefore, the rate of change, viz. Gamma is the same for both call and put options. For example 6. The movement in gamma of the option mentioned in Example 6. Gamma is high when the option is at the money. However, it declines as the option goes deep in the money or out of the money. The graph looks like the normal distribution bell-shaped curve, though it is not symmetrical. The longer extension on the right side implies that for the same difference between stock price and exercise price, in the money calls and out of the money puts have higher gamma than out of the money calls and in the money puts.

With the passage of time, the option gets closer to maturity. Theta is the sensitivity of the value of the option with respect to change in time to maturity assuming everything else remains the same. Per day value of Theta which is more meaningful is calculated by dividing by The value is 0.

Thetais usually negative, because shorter the time to maturity, lower the value of the option. European Call on non-dividend paying stock rKe-rTN d2. Substituting the values from Example 8. Per day value of Theta is 0. Change in value of Theta of both call and put options as the stock price changes can be seen in Figure 6.

Figure 6. Call on a dividend paying stock can have a positive theta. Vega measures the change in option value when the volatility of the stock changes.

The call and put options have the same Vega. The change in Vega for different values of the stock price for the option in Example 6.

As with gamma, it looks like an asymmetric bell-shaped curve. Vega is maximum around the exercise price. Rho measures the sensitivity of the value of an option to changes in the risk free rate. The same formulae can be used even in the case of a dividend-paying stock.

Delta Theta Gamma Rho. Other things remaining the same, Gamma is the same for both call and put contracts True False. Most international transactions entail an exposure to a foreign currency. Importers, exporters, lenders and investors may seek to cover the risks arising out of their foreign currency exposure. Speculaters wish to benefit from expected changes in the exchange rates. As in the case of equity and debt, exposures to currency too can be taken directly or through futures and options.

Currency future is a contract to exchange one currency for another at a specified date in the future at a price exchange rate that is fixed on the purchase date. Currency futures are available on four currency pairs viz. Quantity freeze comes into effect if the order is for more than 10, contracts. Contracts are traded on a 12 month trading cycle. They expire at 12 noon, two working days prior to the last business day of the expiry month.

Initial margin is based on SPAN. Different calendar spread margins are prescribed in rupees for various currencies and contract periods. Daily settlement price is based on weighted average price in last half hour of trading.

Theoretical daily settlement price is computed for unexpired futures contracts, which are not traded during the last half an hour on a day. The final settlement price is the RBI reference rate. Final settlement is on the last business day. The theoretic daily settlement price is given by the following formula: Foreign risk free interest rate is the relevant LIBOR rate or such other rate as may be specified by the Clearing Corporation from time to time.

Suppose, spot USD is at Rs. The value of a 1-year future on the USD is calculated as: Quantity freeze would be applicable beyond 10, such contracts. Suppose X has USD1, He needs to convert it to INR in a year.

He can do the conversion right away, or in a year. Using the same numbers as the previous example, if he does the conversion immediately, he will receive 1, X Rs. Suppose X chooses to do the conversion in 1 year while hedging himself by selling 1-year currency futures. USD 1, At the futures exchange rate, it will amount to Rs. This is the same as the immediate conversion option minor difference being on account of rounding off.

Thus, the futures price calculated represents a no-arbitrage price. If futures were being traded in the market at an underlying exchange rate of Rs. However, if futures were being traded at an underlying exchange rate of Rs. Speculaters in the market ensure that futures prices remain closer to the no-arbitrage price. In the earlier example, there are a few issues to understand: X would have had to sell currency futures worth USD 1, But since the contracts are available in multiples of USD 1,, he will sell 1 contract, and retain an open position for the remaining USD On the sale of currency futures, X would be subject to margin payments.

Initial margin would need to be paid. Thereafter, depending on how the currency moves, he will keep receiving or paying daily MTM margins. The futures contracts are cash settled. Therefore, X will not be able to deliver the USD 1, in the stock exchange. He will sell it to his bank at the spot rate prevailing at the end of 1 year. While the futures contract will be cash settled at the RBI Reference Rate, the spot rate that the bank would give him after 1 year can be slightly different from the RBI Reference Rate.

Instead of currency futures, X can enter into a forward rate agreement with the bank to sell USD at the end of 1 year at a rate that is decided today. The benefit of this approach for X is: X can do the forward rate agreement for odd amounts. He is not constrained by the USD 1, contract unit. Margin payments are avoided. X is also not exposed to a potential gap between the RBI Reference Rate on maturity, and the spot rate that the bank would offer at that time.

However, the following disadvantages of forward rate agreements need to be understood: At the same point of time, various banks offer different exchange rates for the forward contract. There is a lack of transparency in offering these rates, because. Currency futures, on the other hand, are traded in the market, and the prices are transparently available through the net and other media. If the currency were to move in his favour, X can keep receiving margin payments on the currency futures he has sold.

In a forward rate agreement however, X will get the benefit of this favourable movement in exchange rates only at the end of the forward period.

Each contract unit represents 1, USD. The premium is quoted in INR. The last trading day is two working days prior to the last business day of the expiry month, at 12 noon. Final settlement day is the last business day of the expiry month. Strikes are available at intervals of Rs. Quantity freeze kicks in for orders above 10, units. All in-the-money open long contracts are automatically exercised at the final settlement price and assigned on a random basis to the open short positions of the same strike and series.

Initial margin, payable by the seller, is SPAN-based. Final settlement price is the RBI reference rate on the date of expiry of the contract. All contracts are cash settled in rupees. The Black Scholes formulae used for valuing stock options need to be modified to value currency options.

C stands for Call option S0is the current price of the foreign currency i. A 3-month option on USD has exercise price of Rs. Substituting, we get 50 X 0. Thus, from the current spot exchange rate of Rs. DIST 0. Similar problems are included in the Examination] rf T. In the example given earlier, X was committed to an exchange rate, irrespective of whether he converted to INR immediately at Rs 50 , or whether he sold currency futures at Rs.

If the USD were to strengthen considerably, to say, Rs. He would have had to pay an option premium for buying the put option contract which would have given him the right to sell USD 1, The extra money that he will earn by selling the USD at a higher rate would more If the USD were to weaken to say, Rs. The extra money thus earned on the put option, can make up for the loss X would face in selling his USD 1, Similarly, a party Y that needs to make a payment of USD 1, after 1 year, can buy a 1-year call at a strike of Rs.

It will need to pay an option premium. If the USD were to strengthen to say, Rs. The gain on that will cover Y for the higher price at which it will buy the USD from its bank in the cash market. The benefit that it will have of buying USD at this low price will more than cover for the option premium paid.

As in the case of futures, options too are traded in the market. Thus, there is a transparency associated with the pricing of such trades. If GBP is at Rs. What should be the price for a 6-month currency futures contract? Chapter 8 Swaps Swaps are contracts where the two parties commit to exchange two different streams of payments, based on a notional principal.

The payments may cover only interest, or extend to the principal in different currencies or even relate to other asset classes like equity or commodities. Unlike futures and options, which are created and traded in the stock exchanges, swaps are over-the-counter OTC products. These are not traded in a stock exchange. Often a bank finds two parties with divergent views about the market interest rates, exchange rates etc.

The bank performs either of two roles: Broker Here, the swap will be direct between the two parties.

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So the two parties will know each other when the bank brokers the swap. As broker, the bank will earn commission from one or both parties. Dealer Here, the bank executes independent swap trades with both parties. Consequently, neither party will know the identity of the other; for both parties, the bank is the counter-party.

In such trades, the bank earns the difference between the two matching trades. The bank neither has an exposure to MIBOR nor an exposure to fixed interest rate, on account of the combination of the two swaps. The bank is however exposed to credit risk from both parties. Since swaps are OTC products, without the benefit of a transparent pricing benchmark, the spreads can be quite large.

This is the reason parties explore exchange traded futures and options. This is the most elementary form of a swap. Suppose Party A is worried about its 2-year loan of Rs. If interest rates were to go up, it will have to pay higher interest to its lender. On the other hand, Party B is worried that interest rates may fall, and it will earn less on its deposits. Party A and Party B can do an interest rate swap.

While the swap may be direct between Party A and Party B, it is understood better if we bring in a 3rd party viz. Party As Lender.

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The bank that brings Party A and Party B together may be a 4th party. The position of the 3 parties is shown in Figure 8. Figure 8. The actual cash flows of the parties are shown in Table 8. Party As net interest cost is Rs. On the Rs. A few points to note: The swap is a separate transaction between Party A and Party B. Party As lender may not even be aware of the swap. The parties avoid multiple payments by netting. An interest rate swap has only interest payments.

Since no principal is paid, the cash flows are not like a normal coupon bearing bond. However, by assuming a receipt and payment on maturity, the cash flows can be made to look like a coupon bearing bond.

Receipt and payment of the same amount on maturity will net each other. Therefore, it does not affect the economics of the swap in any way, but aids valuing the swap as a bond. If Party A were to pay Rs. Receipt of Rs. It has effectively sold a fixed rate bond and purchased a floating rate bond. The value of the Swap for Party A can be defined as: Valuation Floating. The two bonds can be valued on yield to maturity YTM basis like any debt security.

The swap is normally initiated at prevailing interest rates. Therefore, initially, the value of When yields go up, fixed rate instruments lose value.

Therefore, Valuation for Party A. Party Bs position is reverse. When yields go down, fixed rate instruments gain value. Therefore, Valuation Party B. There is a reason for this. If MIBOR were to change, the floating rate instrument will in any case pay the changed rate for the next interest cycle.

Therefore, it will be at par on the next interest payment date. Suppose that on Jan 1, , the 1-year yield is at 8. Thus, the swap is beneficial to Party A. How much is that benefit? The calculation is shown in Table 8. Table 8. Party B has lost out on the Swap. An alternate approach to valuing swaps is on the basis of FRAs. FRA is an agreement to lend money on a future date at an interest rate that is decided today.

Typically, this is derived from the market as discussed below. In the earlier example, the 1 year yield on Jan 1, was 8. What then, is the yield for the period July 1, to Dec 31, Thus, it can be said that Rs. This translates to a return of This is equivalent to 8. The bond pricing example used a single 8. The FRA approach uses different discount rates for each cash flow. This more complex approach is often used for valuing exotic swaps.

In a currency swap, the two streams of payments are in different currencies. Suppose Party D and Party R, are counter-parties to a 2-year swap. Party Rs cash flows are shown in Table 8. Party D has done the reverse viz. The swap is Fixed for Fixed. As with interest rate swaps, currency swaps too are valued like bonds. The examples in Tables 8. Since the cash flows already resembles a bond structure, there is no need to make any special adjustment for payment of notional principal.

Party Ds position is the reverse viz. Party D will be better off if the rupee strengthens against the USD. A swaption is an option to enter into a swap. He is prepared to take interest risk for 2 years. But, he is worried about interest rates after 2 years. At the end of 2 years, he can do a swap to pay fixed and receive floating. The only problem is that the terms of the swap will depend on the interest rate scenario at that time. Instead, he can enter into a swaption today. This will give him the right, but not an obligation to do the swap after 2 years.

The terms of the underlying swap are decided today, for which he will have to pay an option premium. The borrower, in this case, can be said to have gone long on a call option because he will receive floating under the swap on the swap. Suppose that the original loan agreement was on fixed interest rate basis, and the subsequent swap is for the borrower to pay floating and receive fixed. If the borrower does a swaption, he is said to have gone long on a put option because he will pay floating under the swap on the swap.

Self-Assessment Questions Which of the following roles does a bank perform in swaps? Broker Dealer Either of the above None of the above. The FRA approach to interest rate swap valuation uses different discount rates for each cash flow. Chapter 9 Embedded Options in Debt Instruments 9. The contract is created by the stock exchange. The holder pays an option premium to the writer of the call option. A warrant too entitles the holder to an underlying security at a certain price.

However, unlike a call option, the warrant is issued by the company concerned. If the warrant is exercised, the issuing company will issue fresh securities, thus affecting the balance sheet of the company and the stake of other investors in the company. Warrants are often attached to a debt security, to make it more attractive for the investor, or reduce the interest cost of the issuer. Thus, the investor does not pay a separate price for acquiring the warrant though he will have to pay the agreed price for the security if he chooses to exercise the warrant.

Further, the warrant may not be traded in the stock market. Therefore, it does not have the liquidity and price discovery features normally associated with exchange-created call options.

In the absence of a transparent pricing of the warrant in the market, a round-about route should ideally be adopted for its valuation.

Some other similar company, which has not issued any warrants, is to be taken as a benchmark. Call option on the benchmark companys stock can be valued using Black Scholes or binomial models. Since exercise of the warrant will lead to issue of new securities, the value of the underlying securities is likely to be pulled down. The extent of such value depletion would depend on number of new securities issued. Therefore, the warrant cannot be valued at the same price as the call option of the benchmark company.

The round-about method does post its challenge in terms of identifying a benchmark company. Therefore, the market values warrants like options on stock of the warrant-issuing company and not benchmark company. The Black Scholes call option valuation on this basis is a reasonable approximation of the true value of the warrant, except when the number of warrants is a large proportion of the number of existing shares, and the options are deeply out-of-the-money.

A convertible bond entitles the holder to either get the principal back, or get them converted into a certain number of shares of the company. Conceptually, it can be viewed as a combination of a non-convertible bond and a warrant to convert the redemption proceeds into a certain number of shares. Depending on the price of the underlying and the exercise price, the investor will decide between receiving the money back and using the money to acquire the agreed number of shares.

Convertible bonds are therefore valued as a combination of non-convertible bond and a warrant. Suppose a stock which is trading at Rs. These are due to mature in 3 months. Interest is paid quarterly. The investor has the option to convert each bond into 1, shares at Rs.

Interest payable on the bond at the end of 3 months would be Rs. Thus, redemption amount would be Rs. Valuation as a non-convertible bond would entail discounting the redemption amount by the companys borrowing rate. The warrant is similar to the call option for 1 share that was described in Example 5. In that example, the call option was valued at Rs. Since the debenture is convertible into 1, shares, the option valuation is 1, X Rs. Call option, as already discussed, gives the holder of the option, the right to buy a security at a specified price.

The holder of the call pays an option premium to the writer of the call. Debt securities are often issued with an option to the issuer to call back the security, as provided in the terms of issue of the debt security. This means that P has the option of redeeming the debenture, at par, at the end of 3 years, instead of its normal term of 5 years.

Thus, the call is most likely to be exercised, if yields in the market were to go down. In the normal course, if yields in the market were to go down, then price of fixed interest rate debt securities would go up Thin sloping line in Figure 9. Thus, the investor can earn a capital gain.

The call option or the issuer limits this upside potential for the investor. The thick horizontal line in Figure 9. It is unlikely that the price will go above this line, because the issuer will call back the security at the call price, if yields in the market decline to that extent.

Figure 9. A debenture of 5 years, with call option at the end of 3 years, effectively has a swaption built in. The issuer has the option to swap his interest rate liability to the then prevailing interest rates, at the end of 3 years. Put option, as already discussed, gives the holder of the option, the right to sell a security at a specified price. The holder of the put pays an option premium to the writer of the put.

Debt securities are often issued with an option to the investor to put the security back to the issuer, as provided in the terms of issue of the debt security. This means that the investor has the option of seeking redemption of the debenture, at par, at the end of 3 years, instead of its normal term of 5 years.

Thus, the put is most likely to be exercised, if yields in the market were to go up. In the normal course, if yields in the market were to go up, then price of fixed interest rate debt securities would go down Thin sloping line in Figure 9. Thus, the investor may book a capital loss. The put option with the investor limits his downside.

Suppose the thick horizontal line in Figure 9. It is unlikely that the price of the debenture will go below this line, because the investor can put it back to the issuer at the put price, if yields in the market increase to that extent.

An investor in a debenture that has a call option is at a disadvantage as compared to an investor in a debenture that does not have the call option. This is particularly so, if the call is at par. The investor in the debenture with call option would therefore expect some compensation, either in terms of higher interest rate or a redemption premium, if the call is exercised.

Similarly, the issuer would expect to offer a lower interest rate on a debenture that has a put. Else, the issuer would at least seek to structure the instrument with the redemption being at a discount, if the put is exercised. Issuer may balance this by offering a call and put in the instrument on the same date. In that case, the instrument is likely to be redeemed early. Either yields in the market may go down, in which case the call will get exercised; or yields in the market may go up, in which case the put will get exercised.

In a floating rate instrument, the interest payable by the issuer keeps going up with the benchmark. Issuers who wish to put a limit to their interest cost will set a cap. In the above case, the cap was embedded in the debenture. It was part of the terms of the debenture issue. Caps can also be purchased. Suppose the issuer in the above case issued an uncapped debenture. It will look for someone who is prepared to sell a cap. The cap seller will not have to pay the issuer anything.

The consideration received for selling the cap to the cap buyer will be an income for the cap seller. In option terminology, the receipts for the cap-buyer from the cap can be defined as Max 0, R k , where R is the interest payable on the debenture K is the cap rate The cap is thus like a call option, where the cap buyer benefits if interest rates go above a level; else he does not receive anything under the cap. Only the premium for purchase of cap needs to be borne.

The pay-off matrix for the cap buyer and cap seller are shown in Figures 9.

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Assumption is debenture issue of Rs. Cap buyer incurs the premium of Rs. The premium is the net loss. This offsets the option premium of Rs. Therefore the net pay off is nil. The same economics will work on each interest payment date. Thus, the issuer would have bought a series of caps; each of them is called a caplet. A Cap agreement can be seen as a series of caplets. The pay-off for the cap-seller is the reverse, as seen in Figure 9. Cap seller receives the premium of Rs.

The premium is the net profit. This offsets the option premium income of Rs. Just as cap protects the issuer, floor protects the investor in a floating rate debenture. If that is not available, then he can buy a floor from a floor seller. Suppose he does that. He buys a floor at, say, Rs. He only bears the option premium. In option terminology, the receipts for the floor-buyer from the floor can be defined as Max 0, K R , where R is the interest payable on the debenture K is the floor rate The floor is thus like a put option, where the floor buyer benefits if interest rates go below Only the premium for purchase of floor needs to be borne.

The pay-off matrix for the floor buyer and floor seller are shown in Figures 9. Assumption is debenture investment of Rs. Thus, the invester would have bought a series of floors; each of them is called a floorlet. A Floor agreement can be seen as a series of floorlets.

The pay-off for the floor-seller is the reverse, as seen in Figure 9. Floor seller receives the premium of Rs. The cap and floor can be set at a level where the option premia receivable and payable match. This will make it a zero cost collar. Debentures issued with a floor and cap, effectively have an embedded collar.

The issuer has purchased a cap from the investor and sold a floor to the investor. With this collar, the issuer ensures that his borrowing cost will remain between the floor and the cap. If the debenture does not have an embedded cap, floor or collar, the investor can buy a floor and sell a cap.

Depending on the floor and cap rates, he can structure a zero cost collar for himself. Self-Assessment Questions Company A has issued 10 lakh shares and warrants, which on exercise will lead to another 2 lakh shares. The benchmark company Xs call options are valued at Rs. What should be the value of Company As warrants?

Interest is payable semi-annually. Each debenture is convertible into 10 shares at the option of the investor. Call options of the company with strike of Rs. The convertible debentures represent a small portion of Company Xs share capital. What is the value of the convertible debenture? For instance, Party B may buy bonds issued by Party S.

Party B is exposed to a credit risk on Party S, until the bonds are redeemed. Party A may loan money to Party D that is repayable in a few years. Parties P and Q may enter into a swap. The examples given earlier showed separately, the amounts payable on each leg of the swap. In practice, a single net payment is made by one party to the other, depending on how the interest rates and or exchange rates move.

The party which is to receive the net payment is exposed to a credit risk on the swap counter-party. They evaluate borrowing programs such as a specific series of debenture issue and award a credit rating, which is denoted by a symbol.

The credit rating symbols are different for different types of borrowings, such as short term or long term. Table Where a rating is not based on balance sheet of the borrower but a specific credit enhancement structure that has been put in place, the symbol is succeeded by SO which stands for Structured Obligation. Issuers with poor credit rating offer higher rates of interest on their debt issues. In other words, they offer higher yield spreads spread over sovereign yields.

This is an attraction for investors to go beyond sovereign securities and take the credit risk. However, it is important for the investor to judge the credit risk prudently. Credit risk can cause serious damage to the balance sheet of the investor, if there is a default. Even if there is no default, deterioration in the credit rating of the issuer can raise yield expectations from that company in the market. When the yield expectation goes up, the debt security will lose value.

Consequently, the investor may have to book mark to market losses. Such instruments carry lowest credit risk. Instruments with this rating are considered to have high degree AA High safety of safety regarding timely servicing of financial obligations.

Such instruments carry very low credit risk. Instruments with this rating are considered to have adequate A Adequate safety degree of safety regarding timely servicing of financial obligations.

Such instruments carry low credit risk. Instruments with this rating are considered to have moderate BBB Moderate safety degree of safety regarding timely servicing of financial obligations. Such instruments carry moderate credit risk. BB Moderate risk B High risk C Very high risk D Default Instruments with this rating are considered to have moderate risk of default regarding timely servicing of financial obligations.

Instruments with this rating are considered to have high risk of default regarding timely servicing of financial obligations. Instruments with this rating are considered to have very high risk of default regarding timely servicing of financial obligations. Instruments with this rating are in default or are expected to be in default soon. For example, AAA may not have defaulted within 2 years of the rating; however 0.

When a company goes bankrupt, how much were creditors able to recover. This is given by the Recovery Rate. Bond valuations in the market are commonly used for this purpose. Two approaches are shown below:. Interest is payable semi-annual. The tenor is 5 years. What is the default rate for Company Xs bonds, according to the bond market?

The calculations are shown in Table The valuation on risk-free basis is The difference, Rs. Company X can default on its bonds any day during the 5 years. For simplicity in calculation, let us do the workings on each interest payment date, assuming that the immediate coupon will be received.

Let us also assume that the default probability is P on each interest payment date. The expected loss from default, as per present value calculations are shown in Table To understand the calculations, let us examine the position at Time 4. Expected cash flows are: Coupon of Rs.

We need to find the present value of that loss, for which the risk-free discount factor for Year 4 is 0. The present value of the Year 4 loss is therefore Rs. Since probability of default is P, the present value of expected loss is Rs. The total of similar calculations for each interest payment date is This represents the expected loss at Time 0, which we calculated as Rs. Therefore, The probability of default on Company Xs bonds is 2. Creating a charge on fixed assets of adequate value Seeking pledge of the companys shares having voting rights Seeking a guarantee from the promoters Creating a structured obligation, where the customers of the borrower deposit money into a specific bank account over which the lender has an escrow facility Buying a credit default swap Sell the credit risk through alternate structures like Collateralised Debt Obligation CDO.

A CDS has two parties buyer and seller. The buyer Party B in the earlier example pays premium to the seller say, Bank X for the protection. In return, the seller promises to compensate the buyer, if the issuer Party S in the earlier example of the underlying bond defaults on the payments. CDS sold without proper credit risk assessment led several CDS sellers to bankruptcy in the developed markets in the last few years.

RBI has therefore imposed a strict regulatory regime for the product. The key regulations are as follows: Participants in the market are classified into two: These entities are permitted to buy credit protection buy CDS contracts only to hedge their underlying credit risk on corporate bonds. Such entities are not permitted to hold credit protection without having eligible underlying as a hedged item. Users are also not permitted to sell protection and are not permitted to hold short positions in the CDS contracts.

However, they are permitted to exit their bought CDS positions by unwinding them with the original counterparty or by assigning them in favour of buyer of the underlying bond. Insurance companies and Mutual Funds would be permitted as market-makers subject to their having strong financials and risk management capabilities as prescribed by their respective regulators IRDA and SEBI and as and when permitted by the respective regulatory authorities.

They are permitted to buy protection without having the underlying bond. Detailed eligibility criteria have been specified for every category of market maker. In case a market-maker fails to meet one or more of the eligibility criteria subsequent to commencing the CDS transactions, it would not be eligible to sell new protection.

As regards existing contracts, such protection sellers would meet all their obligations as per the contract. The party against whose default, protection is bought and sold through a CDS is called the reference entity.

CDS is allowed only on the following reference obligations: Such SPVs need to make disclosures on the structure, usage, purpose and performance of SPVs in their financial statements. The reference obligations are required to be in dematerialised form only. The reference obligation of a specific obligor covered by the CDS contract should be specified a priori in the contract and reviewed periodically for better risk management.

Users cannot buy CDS for amounts higher than the face value of corporate bonds held by them and for periods longer than the tenor of corporate bonds held by them. They shall not, at any point of time, maintain naked CDS protection i. CDS purchase position without having an eligible underlying.

Proper caveat has to be included in the agreement that the market-maker, while entering into and unwinding the CDS contract, needs to ensure that the user has exposure in the underlying. Users cannot exit their bought positions by entering into an offsetting sale contract.

They can exit their bought position by either unwinding the contract with the original counterparty or, in the event of sale of the underlying bond, by assigning novating the CDS protection, to the purchaser of the underlying bond the transferee subject to consent of the original protection seller the remaining party. After assigning the contract, the original buyer of protection the transferor will end his involvement in the transaction and credit risk will continue to lie with the original protection seller.

In case of sale of the underlying, every effort should be made to unwind the CDS position immediately on sale of the underlying. The users are given a maximum grace period of ten business days from the date of sale of the underlying bond to unwind the CDS position.

In the case of unwinding of the CDS contract, the original counterparty protection seller is required to ensure that the protection buyer has the underlying at the time of unwinding. The protection seller should also ensure that the transaction is done at a transparent market price and this must be subject to rigorous audit discipline.

CDS transactions are not permitted to be entered into either between related parties or where the reference entity is a related party to either of the contracting parties. In the case of foreign banks operating in India, the term related parties includes an entity which is a related party of the foreign bank, its parent, or group entity. The user except FIIs and market-maker need to be resident entities. CDS Contracts o The identity of the parties responsible for determining whether a credit event has occurred must be clearly defined a priori in the documentation.

CDS cannot be written on interest receivables. CDS cannot be written on securities with original maturity up to one year e. The CDS contract must represent a direct claim on the protection seller. The CDS contract must be irrevocable; there must be no clause in the contract that would allow the protection seller to unilaterally cancel the contract. The CDS contract should not have any clause that may prevent the protection seller from making the credit event payment in a timely manner, after occurrence of the credit event and completion of necessary formalities in terms of the contract.

The CDS contracts need to be standardized. The standardisation of CDS contracts in terms of coupon, coupon payment dates, etc. The credit events specified in the CDS contract may cover: Further, the definition of various credit events should be clearly defined in the bilateral Master Agreement.

At least 25 per cent of the members should be drawn from the users. The decisions of the Committee are binding on CDS market participants. For transactions involving users, physical settlement is mandatory.

For other transactions, market-makers can opt for any of the three settlement methods physical, cash and auction , provided the CDS documentation envisages such settlement. Auction settlement may be conducted in those cases as deemed fit by the DC. Auction specific terms e. If parties do not select Auction Settlement, they will need to bilaterally settle their trades in accordance with the Settlement Method unless otherwise freshly negotiated between the parties. However, if a proprietary model results in a more conservative valuation, the market participant can use that proprietary model.

For better transparency, market participants using their proprietary model for pricing in accounting statements have to disclose both the proprietary model price and the standard model price in notes to the accounts that should also include an explanation of the rationale behind using a particular model over another. The participants need to put in place robust risk management systems. Market-makers have to ensure adherence to suitability and appropriateness criteria while dealing with users.

CDS transactions must be conducted in a transparent manner in relation to prices, market practices etc. From the protection buyers side, it would be appropriate that the senior management is involved in transactions to ensure checks and balances. Protection sellers need to ensure:. CDS transactions are undertaken only on obtaining from the counterparty, a copy of a resolution passed by their Board of Directors, authorising the counterparty to transact in CDS.

The product terms are transparent and clearly explained to the counterparties along with risks involved. Market-makers have to report their CDS trades with both users and other marketmakers on the reporting platform of the CDS trade repository within 30 minutes from the deal time. The users are required to affirm or reject their trade already reported by the market maker by the end of the day.

In the event of sale of underlying bond by the user and the user assigning the CDS protection to the purchaser of the bond subject to the consent of the original protection seller, the original protection seller has to report such assignment to the trade reporting platform and the same should be confirmed by both the original user and the new assignee.

The SPV splits the expected cash flows from the portfolio into various tranches, as shown in Figure Each tranche is sold to different classes of investors, based on their risk appetite.

Thus, Tranche 2 is less risky than Tranche 1. In most prudent portfolios, this is a remote possibility. Therefore, the principal of investors in Tranche 3 is better protected.

Each tranche is given a separate credit rating. Such CDO structures were a major cause for the global financial crisis in Lenders originated several loans of dubious quality and sold them off as CDOs. The credit quality of some of these tranches was enhanced by buying CDS from institutions that did not fully understand the risks involved. Credit Rating agencies too did not fully appreciate the portfolio risk and the risk of CDS-sellers defaulting. This shook the confidence of investors and lenders.

It is for this reason that investors need to fully comprehend the complex structures in which they invest, and not go blindly by the credit rating of the investment. This also explains why the regulatory authorities in India are cautious in approving new product structures. It is widely recognised that such a cautious approach helped in protecting India from any direct fallout from the global financial crisis.

As is inevitable in a globalised world, India did face, and continues to face, the indirect fallout of risk aversion, freezing of credit markets and recession in US and Europe. Self-Assessment Questions Which of the following is good for the investor? Higher default risk Higher recovery rate Both the above None of the above. What is the default risk according to the market?

What is the expected loss in the debentures as per the market? Which of the following does not help mitigate credit risk? Which of the following is not permitted to be CDS market maker? Annexure 2: Important Formulae 1. Flag for inappropriate content. Related titles. Jump to Page. Search inside document.

Higher the spot price, higher the intrinsic value of the call. Share Prices Lognormal Distribution Share prices can go up to any level, but they cannot go below zero.

Historical Volatility More the data points, better the estimate of historical volatility. Estimate s of standard deviation of daily return, tis given by i. Broadly, the model can be defined as follows: Exponentially Weighted Moving Average EWMA The ARCH m model can be simplified by assuming that the weights i decrease exponentially by a constant factor, for every prior observation, where is a constant that takes a value between 0 and 1.

Implied Volatility The volatility estimation discussed so far considered historical volatility based on price movement of a market variable, such as price of a stock. True False The value of e is 2. On the NSE, futures are available on: A contract offering a perfect hedge may not be available The contract offering a perfect hedge may be less liquid The contract offering a perfect hedge may not be available for the desired maturity The contract offering a perfect hedge may be costlier to transact When the asset used for hedging is different from the asset being hedged, it is called crosshedging.

In this Chapter o o o o Going long with futures Going short with futures Hedging with futures Modifying portfolio beta Previous Chapter o o Cash and carry arbitrage Reverse cash and carry arbitrage Derivatives can pose unique challenges in terms of margin payments and periodic booking of profits or losses, especially in the case of rolling hedges. Long in cash market Long in futures market Both the above Short in cash market and futures market An investor has bought a stock worth Rs.

The GoI security should have minimum total outstanding stock of Rs. Expiry of Contracts FUTIRT contracts are permitted for every month for the first 3 months, and thereafter every quarter for 3 quarters. Pricing terminology Prices are quoted in the market at Futures Discount Yield. Similar problems are included in the Examination] rf T N -d1 7. This will raise the value of the swap for in determining the value of the swap has not been highlighted.

Therefore, it is the that drive the value of the swap. The value of swap for Party A is Valuation i. True False Call option is likely to be exercised if yields were to go up. Two approaches are shown below: The protection seller shall have no recourse to the protection buyer for creditevent losses.