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Chapter 17

Chapter 17. Non-Generic Interest Rate and Currency Swaps. Non-Generic Swaps. While approximately 80% of all interest rate swaps are generic, the underlying structure of the generic swap has been modified in a number of ways to accommodate different uses.

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Chapter 17

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  1. Chapter 17 Non-Generic Interest Rate and Currency Swaps

  2. Non-Generic Swaps • While approximately 80% of all interest rate swaps are generic, the underlying structure of the generic swap has been modified in a number of ways to accommodate different uses. • Non-generic swaps usually differ in terms of their rates, principal, or effective dates. • The next four slides summarizes some of the common non-generic swaps.

  3. Non-Generic Swaps

  4. Non-Generic Swaps

  5. Non-Generic Swaps

  6. Non-Generic Swaps

  7. Non-Generic Swaps • Of the non-generic swaps, the two most extensively used ones are: • Forward Swap • Swaption

  8. Forward Swap • A forward swap is an agreement to enter into a swap that starts at a future date at an interest rate agreed upon today. • Like futures contracts on debt securities, forward swaps provide borrowers and investors with a tool for locking in a future interest rate.

  9. Hedging a Future Loan • Example: A company wishing to lock in a rate on a five-year, fixed-rate $100 loan to start two year from today, could enter a two-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 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.

  10. Hedging a Future Loan

  11. Hedging a Future Loan • Alternatively, at the forward swap’s expiration date, the company could sell the five-year 9%/LIBOR swap underlying the forward swap contract and issue five-year fixed-rate debt. • If the rate on five-year fixed rate bonds 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 five-year annuity equal to 1% (difference in rates: 10%-9%) times the NP.

  12. Hedging a Future Loan • For example, at 10% the value of the underlying 9%/LIBOR swap would be $3.8609 per $100 NP using the YTM swap valuation approach: • With the proceeds of $3.8609 from closing its swap, the company would only need to raise $96.1391 (= $100 - $3.8609). • The company, though, would have to issue $96.1391 worth of 5-year fixed-rate bonds at the higher 10% rate. This would result in semiannual interest payments of $4.8070 (= (.10/2)($96.1391).

  13. Hedging a Future Loan • Using the ARR and assuming a flat yield curve, the company’s effective rate based on the $100 funds needed would be 9.2%:

  14. Hedging a Future Loan • If the rate on five-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 five-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 using the YTM approach:

  15. Hedging a Future Loan • The company would therefore have to pay the swap bank $4.055 for assuming its fixed-payer’s position. • With a payment of $4.055, the company would need to raise a total of $104.055 from it bond issue. • The company, though, would be able to issue $104.055 worth of 5-year fixed-rate bonds at the lower rate of 8% rate.

  16. Hedging a Future Loan • Its semiannual interest payments would be $4.1622 (= .08/2)($104.055), and its ARR based on the $100 funds needed would be 8.8%:

  17. Hedging a Future Loan • The exhibit summarizes the swap values, loanable funds needed, semiannual interest payments, and ARRs based on the $100 funds needed by the company given several interest rate cases. • As shown, the forward swap enables the company to lock in a borrowing rate of approximately 9%. • Note: Valuing the swap using the YTM approach results in hedged ARRs that are close to 9%, but are not equal.

  18. Hedging a Future Loan

  19. 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 $10M cash inflow one year from now in a five-year, high quality fixed-rate bond. • The investor could lock in the future rate by entering a one-year forward swap agreement to receive the fixed rate and pay the floating rate on a five-year, 9%/LIBOR swap with a NP of $10M.

  20. Hedging a Future Investment • At the expiration date on the forward swap, the investor could invest the $10M cash inflow in a five-year FRN at LIBOR that, when combined with the floating position on the swap, would provide the investor with a synthetic fixed rate-loan paying 9%.

  21. Hedging a Future Investment

  22. Hedging a Future Investment • Instead of a synthetic fixed investment position, the investor alternatively could sell the three-year 9%/LIBOR swap underlying the forward swap contract and invest in a five-year fixed rate note. • If the rate on the five-year fixed rate note were lower than the 9% swap rate, then the investor would be able sell his floating position at a value equal to the present value of an annuity equal to the $10M NP times the difference between 9% and the rate on three-year fixed rate bonds; this gain would offset the lower return on the fixed-rate bond.

  23. Hedging a Future Investment • Example: If at the forward swaps’ expiration date, the rate on three-year, fixed rate bonds were at 8%, and the fixed rate on a three-year par value swap were at 8%, then the institution investment firm would be able to sell its floating-payers position on the three-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%):

  24. Hedging a Future Investment • The investment firm would therefore invest $10M plus the $262,107 proceeds from closing its swap in 3-year, fixed rate bond yielding 8%. Assuming a flat yield curve, the ARR based on a $10M investment is 8.9%:

  25. Hedging a Future Investment • On the other hand, if the rate on three-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 swaps’ expiration date, the rate on three-year, fixed rate bonds were at 10% and the fixed rate on a three-year par value swap were at 10%, then the institution investment firm would have to pay the swap bank $253,785 for assuming its floating-payers position on the three-year 9%/LIBOR swap underlying the forward swap contract:

  26. Hedging a Future Investment • The investment firm would therefore invest $9,746,215 ($10M minus the $253,785 costs incurred in closing its swap) in three-year, fixed rate bonds yielding 10%. Assuming a flat yield curve, the ARR based on a $10M investment would be 9.1%: • The exhibit summarizes the swap values, investment funds, and ARRs based on the $10M investment given several interest rate cases. As shown, the forward swap enables the investment fund to lock in an investment rate of approximately 9%.

  27. Hedging a Future Investment

  28. Using of Forward Swaps to Call a Deferred Callable Bonds • Consider a company with an existing 10%, fixed-rate debt having ten years remaining to maturity, but not callable for three more years. • Suppose that as a result of the low interest rates currently the company expects rates to increase in the future and would like to call its bonds now. • While the company cannot call its debt for three years, it can take advantage of the current low rates by using a forward swap.

  29. Using of Forward Swaps to Call Deferred Callable Bonds • In this case, suppose the company enters into a three-year forward swap agreement to pay fix on a seven-year, 8%/LIBOR swap with a NP equal to the par value of its current ten-year, 10% fixed rate debt (7-year swap, 3 years forward).

  30. Using of Forward Swaps to Call Deferred Callable Bonds • Three years later, if rates are lower than 10%, the company could issue flexible-rate debt to finance the call of its 10% fixed debt. This action, combined with its fixed payer’s position on the 8%/LIBOR swap obtained from its forward swap, would give the company an effective fixed rate of 8%. • On the other hand, if rates are higher than 10% on the call date, the company would not call its debt, but it would be able to offset its 10% debt by selling its 8%/LIBOR swap at a premium.

  31. Using of Forward Swaps to Call Deferred Callable Bonds • Thus, by using a three-year forward agreement on a seven-year swap, the company is able to take advantage of a period of low interest rates to refinance its long-term debt. • This opportunity would not have been possible using more standardized, shorter-term, exchange-traded futures contracts.

  32. Valuation of Forward Swaps • The value of a forward swap depends on whether the rate on the forward contract’s underlying swap is different than its break-even forward swap rate. • The break-even rate on a generic swap is that rate that equates the present values of the fixed and floating cash flows, with the floating cash flows estimated as implied forward rates generated from the zero coupon rates on swaps.

  33. Swap Valuation: Break-Even Swap Rate

  34. Valuation of Forward Swaps • For example, using the estimated zero coupon rates and one-year implied forward rates shown in the next exhibit, the break-even rate on the three-year swap is 5.7%.

  35. Swap Valuation

  36. Swap Valuation: Implied Forward Swap Rates

  37. Swap Valuation: Break-Even Swap Rate

  38. Valuation of Forward Swaps • Like the break-even rate on a generic swap, the break-even rate on a forward swap, Cf*, is that rate that equates the present value of the fixed-rate flows to the present value of floating-rate flows corresponding to the period of the underlying swap.

  39. Valuation of Forward Swaps • Consider a two-year 7%/LIBOR swap, three years forward, in which the applicable zero swap yield curve and corresponding implied forward rates are the ones shown in the preceding exhibit.

  40. Valuation of Forward Swaps • The break-even forward rate for this two-year 7%/LIBOR swap, three years forward is found by solving for that coupon rate, Cf*, that equates the present value of the forward swap’s future fixed–rate payments of Cf* in years four and five to the present value of the implied one-year forward rates three years and four years from the present (f13 = .07697 and f14 = .08891). • Assume that the first effective date on the underlying swap starts at the expiration of the forward swap) in years four and five.

  41. Valuation of Forward Swaps • That is, find Cf* where:

  42. Valuation of Forward Swaps • Substituting the implied forward rates and zero coupon rates into the above equation, we obtain an 8% break-even forward rate for the two-year 7%/LIBOR swap, three years forward:

  43. Valuation of Forward Swaps • Given the specified fixed rate on the forward swap is at 7% and not at its break-even rate of 8%, the fixed payer’s position on the underlying swap would have a value beginning in year four equal to the annual 1% rate differential times the swap’s NP for two years.

  44. Valuation of Forward Swaps • The present value of this cash flow is equal to 1.5071% times the NP or 151.71 BP. Thus, the current value of the two-year 7%/LIBOR swap three years forward is therefore 150.71 BP times the NP:

  45. Valuation of Forward Swaps • If the NP on the swap is $10M, then the value of the forward swap would be $150,710. • Note, if the forward swap rate had been set equal to the 8% break-even rate, then the economic value of the forward swap would be zero.

  46. Swaption • 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 (strike) 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.

  47. Swaption The swaption can be either a call or a put: • A call swaption gives the holder the right to receive a specific fixed rate and pay the floating rate • that is, the right to take a floating payer’s position • A put swaption gives the holder the right to pay a specific fixed rate and receive the floating rate • that is, the right to take a fixed payer’s position

  48. Swaption 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.

  49. Swaption • 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 one-year swap in three 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.

  50. Swaption • Like interest rate and debt options, swaptions can be used for: • Speculating on interest rates • Hedging debt and asset positions against market risk • Managing a balance sheet’s exposure to interest rate changes. • Combined with other securities to create synthetic positions

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