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Swap Derivatives: Forward Swaps and Swaptions. Swap Derivatives. Today, there are a number of nonstandard or non-generic swaps used by financial and non-financial corporations to manage their varied cash flow and asset and liability positions.

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## Swap Derivatives: Forward Swaps and Swaptions

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**Swap Derivatives**• Today, there are a number of nonstandard or non-generic swaps used by financial and non-financial corporations to manage their varied cash flow and asset and liability positions. • Two of the most widely used non-generic swaps are the forward swapand options on swaps or swaptions. • A forward swap is an agreement to enter into a swap that starts at a future date at an interest rate agreed upon today. • A swaption, in turn, is a right, but not an obligation, to take a position on a swap at a specific swap rate.**Forward Swaps**• Like futures and farward contracts on debt securities, forward swaps provide borrowers and investors with a tool for locking in a future interest rate. • As such, they can be used to manage interest rate risk for fixed-income positions.**Hedging a Future Loan with a Forward Swap**• Financial and non-financial institutions that have future borrowing obligations can lock in a future rate by obtaining forward contracts on fixed-payer swap positions.**Hedging a Future Loan**Example: • A company wishing to lock in a rate on a 5-year, fixed-rate $100,000,000 loan to start two years from today, could enter a 2-year forward swap agreement to pay the fixed rate on a five-year 9%/LIBOR swap. • At the expiration date on the forward swap, the company could issue $100,000,000 floating-rate debt at LIBOR that, when combined with the fixed position on the swap, would provide the company with a synthetic fixed rate loan paying 9% on the floating debt.**Hedging a Future Loan**• Alternatively, at the forward swap’s expiration date, the company could sell the 5-year 9%/LIBOR swap underlying the forward swap contract and issue a 5-year fixed-rate bond. • If the rate on 5-year fixed rate bond were higher than 9%, for example at 10%, then the company would be able offset the higher interest by selling its fixed position on the 9%/LIBOR swap to a swap dealer for an amount equal to the present value of a 5-year annuity equal to 1% (difference in rates: 10% − 9%) times the NP.**Hedging a Future Loan**• For example, at 10% the value of the underlying 9%/LIBOR swap would be $3.8609 million using the YTM swap valuation approach:**Hedging a Future Loan**• With the proceeds of $3.8609 million from closing its swap, the company would only need to raise $96.1391 million (= $100 million − $3.8609 million). • The company, though, would have to issue $96.1391 million worth of 5-year fixed-rate bonds at the higher 10% rate. • This would result in semiannual interest payments of $4.8070 million (= (.10/2)($96.1391 million),and the total return based on the $100 million funds needed would be approximately 9%.**Hedging a Future Loan**• If the rate on 5-year fixed rate loans were lower than 9%, say 8%, then the company would benefit from the lower fixed rate loan, but would lose an amount equal to the present value of a 5-year annuity equal to 1% (difference in rates: 8% − 9%) times the NP when it closed the fixed position. • Specifically, at 8%, the value of the underlying 9%/LIBOR swap is −$4.055 million using the YTM approach:**Hedging a Future Loan**• The company would therefore have to pay the swap bank $4.055 million for assuming its fixed-payer’s position. • With a payment of $4.055 million, the company would need to raise a total of $104.055 million from its bond issue. • The company, though, would be able to issue $104.055 million worth of 5-year fixed-rate bonds at the lower rate of 8% rate. • Its semiannual interest payments would be $4.1622 million (= .08/2)($104.055 million), and its total return based on the $100 million funds needed would be approximately 9%.**Hedging a Future Investment**• Forward swaps can also be used on the asset side to fix the rate on a future investment. • Consider the case of an institutional investor planning to invest an expected $10 million cash inflow one year from now in a 3-year, high quality fixed-rate bond. • The investor could lock in the future rate by entering a 1-year forward swap agreement to receive the fixed rate and pay the floating rate on a 3-year, 9%/LIBOR swap with a NP of $10 million.**Hedging a Future Investment**• At the expiration date on the forward swap, the investor could invest the $10 million cash inflow in a 3-year FRN at LIBOR that, which when combined with the floating position on the swap, would provide the investor with a synthetic fixed rate-loan paying 9%.**Hedging a Future Investment**• Instead of forming a synthetic fixed investment position, the investor alternatively could sell the 3-year 9%/LIBOR swap underlying the forward swap contract and invest in a 3-year fixed-rate note. • If the rate on the 3-year fixed rate note were lower than the 9% swap rate, then the investor would be able to sell his floating position at a value equal to the present value of an annuity equal to the $10 million NP times the difference between 9% and the rate on 3-year fixed rate bonds; this gain would offset the lower return on the fixed-rate bond.**Hedging a Future Investment**Example: • If at the forward swaps’ expiration date, the rate on 3-year, fixed rate bonds were at 8%, and the fixed rate on a 3-year par value swap were at 8%, then the investment firm would be able to sell its floating-payer’s position on the 3-year 9%/LIBOR swap underlying the forward swap contract to a swap bank for $262,107 (using the YTM approach with a discount rate of 8%):**Hedging a Future Investment**• The investment firm would therefore invest $10 million plus the $262,107 proceeds from closing its swap position. • The total return based on an investment of $10 million, though, would be approximately equal to 9%.**Hedging a Future Investment**• On the other hand, if the rate on 3-year fixed-rate securities were higher than 9%, the investment company would benefit from the higher investment rate, but would lose on closing its swap position. • Example: If at the forward swap’s expiration date, the rate on 3-year, fixed rate bonds were at 10% and the fixed rate on a 3-year par value swap were at 10%, then the investment firm would have to pay the swap bank $253,785 for assuming its floating-payer’s position on the 3-year 9%/LIBOR swap underlying the forward swap contract:**Hedging a Future Investment**• The investment firm would therefore invest $9,746,215 ($10,000,000 minus the $253,785 costs incurred in closing its swap) in 3-year, fixed rate bonds yielding 10%. • The total return based on an investment of $10 million funds, though, would be approximately equal to 9%.**Other Uses of Forward Swaps**• The examples illustrate that forward swaps are like futures on debt securities. • As such, they are used in many of the same ways as futures: • Locking in future interest rates • Speculating on future interest rate changes • Altering a balance sheet’s exposure to interest rate changes • Different from futures, though, forward swaps can be customized to fit a particular investment or borrowing need and with the starting dates on forward swaps ranging anywhere from one month to several years, they can be applied to not only short-run but also long-run positions.**Swaptions**• One of the most innovative non-generic swaps is the swap option or simply swaption. • As the name suggests, a swaption is an option on a swap. • The purchaser of a swaption buys the right to start an interest rate swap with a specific fixed rate or exercise rate, and with a maturity at or during a specific time period in the future. • If the holder exercises, she takes the swap position, with the swap seller obligated to take the opposite counterparty position. • For swaptions, the underlying instrument is a forward swap and the option premium is the up-front fee.**Swaptions**• The swaption can be either a receiver swaption or a payer swaption: • A receiver swaption gives the holder the right to receive a specific fixed rate and pay the floating rate • The right to take a floating payer’s position • A payer swaption gives the holder the right to pay a specific fixed rate and receive the floating rate • The right to take a fixed payer’s position**Swaptions**Swaptions can be either European or American: • A European swaption can be exercised only at a specific point in time, usually just before the starting date on the swap. • An American swaption is exercisable at any point in time during a specified period of time.**Swaptions**• Swaptions are similar to interest rate options or options on debt securities. They are, however, more varied: • They can range from options to begin a 1-year swap in 3 months to a 10-year option on a 8-year swap (sometimes referred to as a 10 x 8 swaption). • The exercise periods can vary for American swaptions. • Swaptions can be written on generic swaps or non-generic swaps.**Swaptions**• Like interest rate and debt options, swaptions can be used for: • Speculating on interest rates • Hedging debt and asset positions against market risk • Combined with other securities to create synthetic positions**Swaptions: Speculation**• Suppose a speculator expects the rate on high quality, 5-year fixed rate bonds to increase from their current 8% level. • As an alternative to a short T-note futures position or an interest rate call, the speculator could buy a payer swaption.**Swaptions: Speculation**• Suppose the speculator elects to buy a 1-year European payer swaption on a 5-year, 8%/LIBOR swap with a NP of $10,000,00 for 50 bp times the NP: • 1 x 5 payer swaption • Exercise date = 1 year • Exercise rate = 8% • Underlying swap = 5-year, 8%/LIBOR with NP = $10,000,000 • Swap position = fixed payer • Option premium = 50 bp times NP**Swaptions: Speculation**• On the exercise date, if the fixed rate on a 5-year swap were greater than the exercise rate of 8%, then the speculator would exercise her right to pay the fixed rate below the market rate. • To realize the gain, she could take her 8% fixed-rate payer’s swap position obtained from exercising and sell it to another counterparty.**Swaptions: Speculation**• For example, if the 5-year par value swap were trading at 9% and swaps were valued by the YTM approach, then she would be able to sell her 8% swap for $395,636: • If the swap rate at the expiration date were less than 8%, then the payer swaption would have no value and the speculator would simple let it expire, losing the premium she paid.**Swaptions: Speculation**• Formally, the value of the payer swaption at expiration is: • For rates, R, on par value 5-year swaps exceeding the exercise rate of 8%, the value of the payer swaption will be equal to the present value of the interest differential times the notional principal on the swap. • For rates less than or equal to 8%, the swap is worthless. • The next slide shows graphically and in a table the values and profits at expiration obtained from closing the payer swaption on the 5-year 8%/LIBOR swap given different rates at expiration.**Swaptions: Speculation**• Instead of higher rates, suppose the speculator expects rates on 5-year high quality bonds to be lower one year from now. • In this case, her strategy would be to buy a receiver swaption.**Swaptions: Speculation**• If she bought a receiver swaption similar in terms to the above payer swaption (1-year receiver option on a 5-year, 8%/LIBOR swap), and the swap rate on a 5-year swap were less than 8% on the exercise date, then she would realize a gain from exercising and then either selling the floating-payer’s position or combining it with a fixed-payer’s position on a replacement swap.**Swaptions: Speculation**• For example, if the fixed rate on a 5-year par value swap were 7%, the investor would exercise her receiver swaption by taking the 8% floating-rate payer’s swap and then sell the position to another counterparty. • With the current swap rate at 7% she would be able to sell the 8% fixed-payer’s position for $415,830: • If the swap rate were higher than 8% on the exercise date, then the investor would allow the receiver swaption to expire, losing, in turn, her premium.**Swaptions: Speculation**• Formally, the value of the 8%/LIBOR receiver swaption at expiration is • For rates, R, on par value 5-year swaps less than the exercise rate of 8%, the value of the receiver swaption will be equal to the present value of the interest differential times the notional principal on the swap. • For rates equal to or greater than 8%, the swap is worthless. • The next slide shows graphically and in a table the values and profits at expiration obtained from closing the receiver swaption on the 5-year 8%/LIBOR swap given different rates at expiration.**Value and Profit at Expiration from 8%/LBOR ReceiverSwaption****Swaptions: Hedging**• Like other option hedging tools, swaptions give investors or borrowers protection against adverse interest rate movements, but still allow them to benefit if rates move in their favor.**Swaptions: Hedging**• As a hedging tool, swaptions serve as a rate-protection tool: • As rates increase, the value of the payer swaptions increases in value, making the payer swaption act as a cap on the rates paid on debt positions. • As rates decrease, receiver swaptions increase in value, making them act as a floor on the rates earned from asset positions.**Swaptions: Floor**• To illustrate how receiver swaptions are used for establishing a floor, consider the case of a fixed-income investment fund that has a Treasury bond portfolio worth $30,000,000 in par value that is scheduled to mature in 2 years. • Suppose the fund plans to reinvest the $30,000,000 in principal for another 3 years in Treasury notes that are currently trading to yield 6%, but is worried that interest rate could be lower in two years.**Swaptions: Floor**• To establish a floor on its investment, suppose the fund purchased a 2-year receiver swaption on a 3-year, 6%/LIBOR generic swap with a notional principal of $30,000,000 from First Bank for $100,000.**Swaptions: Floor**• The next slide shows: • The values that the fund would obtain from closing its receiver swaption given different rates at the swaption’s expiration. • The hedged total return it would obtain from reinvesting for 3 years the $30,000,000 plus the proceeds from the swaption based on $30,000,000 investment and the assumption of a flat yield curve.**Swaptions: Floor**• As shown in the exhibit slide, for rates less than 6% the swaption values increase as rates fall, in turn, offsetting the lower investment rates and yielding a rate on the investment of approximately 6%. • On the other hand, for rates equal or greater than 6%, the swaption are worthless, whereas the investment’s total return increases as rates increase. • Thus, for the cost of $100,000, the receiver swaption provides the fund a floor with a rate of 6%.**Swaptions: Cap**• In contrast to the use of swaptions to establish a floor on an investment, suppose a firm had a future debt obligation whose rate it wanted to cap. In this case, the firm could purchase a payer swaption. • To illustrate, suppose a company has a $60,000,000, 9% fixed-rate bond obligation maturing in 3 years that it plans to finance by issuing new 5-year fixed-rate bonds. • Suppose the company is worried that interest rates could increase in 3 years and as a result wants to establish a cap on the rate it would pay on its future 5-year bond issue.**Swaptions: Cap**• To cap the rate, suppose the company purchases a 3-year payer swaption on a 5-year, 9%/LIBOR generic swap with notional principal of $60,000,000 from First Bank for $200,000. • The next slide shows for different rates at expiration, the values the company would obtain from closing its payer swaption and the hedged rate (based on $60,000,000 debt and the assumption of a flat yield curve) it would obtain from borrowing for five years the $60,000,000 minus the proceeds from the swaption.**Swaptions: Cap**• As shown in the exhibit slide, for rates greater than 9% the swaption values increase as rates increase, in turn, offsetting the higher borrowing rates and yielding a total return on the hedged bond issue of approximately 9%. • On the other hand, for rates less than 9%, the swaption are worthless whereas the debt’s rate decreases as rates decrease. • Thus, for the cost of $200,000, the payer swaption provides the fund a cap on it future debt with a cap rate of 9%.**Hedging the Risk of Embedded Call Option**• Swaptions can also be used to hedge against the impacts that adverse interest rate changes have on investment and debt positions with embedded options. • Consider a fixed-income manager holding $10,000,000 worth of 10-year, high quality, 8% fixed-rate bonds that are callable in two years at a call price equal to par.**Hedging the Risk of Embedded Call Option**• Suppose the manager expects a decrease in rates over the next two years, increasing the likelihood that his bonds will be called and he will be forced to reinvest in a market with lower rates. • To minimize his exposure to this call risk, suppose the manager buys a 2-year receiver swaption on an 8-year, 8%/LIBOR swap with a NP of $10,000,000.**Hedging the Risk of Embedded Call Option**• If two years later, rates were to increase, then the bonds would not be called and the swaption would have no value. • In this case, the fixed income manager would lose the premium he paid for the receiver swaption.

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