Swaptions

1. Swaptions Chris Dzera

2. Outline Discuss building blocks of swaptions, including some we have discussed in class and some I covered in my previous presentation Define swaptions and give a brief history Explain the important aspects of swaptions and how a swaption works Outline the different types of swaptions Clarify why purchasing swaptions makes sense Give examples of swaption contracts Briefly touch on ways to value swaptions

3. Interest Rate Derivatives An interest rate derivative is a derivative whose payoffs are dependent on future interest rates These are appealing to investors who have specific cashflow needs that are heavily influenced by interest rates The interest rate derivatives market is the largest derivatives market in the world

4. Swaps A swap is an agreement between two companies to exchange cash flows in the future, defining the date the cash flows will be paid and the way they will be calculated Swaps are used to hedge certain risks, such as interest rate risk, or when investors want to speculate about a certain value

5. Interest Rate Swaps The most common type of swap and the most common type of interest rate derivative is a “vanilla” interest rate swap Typically the floating rate in interest rate swap agreements is a fixed rate such as the London Interbank Offered Rate (LIBOR) These swaps usually involve fixed rates being swapped for floating rates, but there are many variations Interest rate swaps allow for hedging of assets and liabilities, as well as speculation by investors

6. Options An option is a derivative contract when a party can elect whether or not they want to exercise the contract The benefit to this is that there is a limited downside for this party For the right to not exercise the contract, the party pays a premium

7. Swaptions A swaption is an option on a swap contract, typically and almost exclusively an interest rate swap The first swaption contract was constructed and executed by William Lawton in 1983 The contract was for a period of one year, and his company sold the right to enter a five year interest rate swap to pay fixed versus 3-month LIBOR on a notional amount of $5 million at a premium Like the building block derivatives discussed earlier swaptions are very popular because they can be used to hedge and they also allow for speculation

8. Components of a Swaption Premium Strike rate (also fixed rate of underlying swap) Length of option period Length of underlying swap Notional amount Amortization, if any Frequency of settlement of payments on the underlying swap

9. How a swaption works Two parties agree to the previously mentioned components The contract holder decides at some date (or multiple dates, depending on the structure of the contract) whether or not they would like to enter the contract before the swap begins or at some point a certain time period into the swap If the holder elects to exercise, a swap contract begins, and if not then the only exchange of payments is the premium

10. Payer Swaption vs. Receiver Swaption Payer swaption– gives the owner of the swaption the right to enter a swap contract where they pay the fixed leg and receive the floating leg Receiver swaption – gives the owner of the swaption the right to enter into a swap contract where they pay the floating leg and receive the fixed leg

11. Exercise Dates There are three different ways the right to exercise the option in a swaption contract can be scheduled European – the owner of the contract can exercise his right to enter the swap at maturity American – the owner of the contract can exercise his right to enter the swap at any date between the start and end dates of the option period agreed to Bermudan – the owner of the contract can exercise his right to enter the swap at certain predetermined dates between the start and end dates of the option period

12. A bit more about American swaptions • There are two types of American swaptions: • An American swaption with fixed tenor is a when the length of the underlying swap is a set amount of time and it begins as soon as the option is exercised, as long as it is exercised before the option period expires • An American swaption with fixed end date is when the predetermined period of time includes the length of the option period and the underlying swap, so if the day the swap would begin passes without the swap being exercised, the length of the underlying swap decreases

13. Why enter a swaption contract versus a swap contract? Because the option period can end before the swap takes place, it may be unclear why it is logical to pay a premium for the option to enter a swap contract down the road when the party could just decide whether or not they want to enter the contract at that later date However, entering a swaption contract assures that the party that holds the contract has the option to receive better terms on the swap contract than they would have if they had waited

14. Example of a European receiver swaption A company knows that in two years it will have to enter a 5 year loan on $5 million with a 2% interest rate, and wants to reduce its interest rate risk by exchanging its payments on this contract for floating payments They enter a swaption contract with a 2 year option period, where at the end of 2 years on the expiry date of the option, if they exercise the option a 5 year swap would be initiated

15. Example of a Bermudan payer swaption A bond holder knows that in one year they will receive fixed rates of 3% on $2 million bond for a period of ten years, and wants to receive a floating rate instead They enter a swaption contract that expires in one year with specific exercise dates afterward that would not go too far into the swap period If they elected to exercise after expiry, the length of the swap would be reduced by the amount of time between the end of the option period and the date the option was exercised

16. Example of an American receiver swaption with fixed tenor A company receives a LIBOR -.02% on a 15 year bond it owns and wants to receive a fixed rate instead They enter a swaption with expiry in 2 years and an underlying swap of length 13 years If they elect to exercise the swap at any time in the option period, a 13 year swap with terms agreed to begins immediately

17. Example of an American payer swaption with fixed end date A company knows it will have to pay a floating rate of LIBOR + .03% on a 30 year loan and wants to pay a fixed rate instead They enter a swaption contract with expiry in 2 years and an end date in 30 years If they elect to exercise the option, a swap that ends when the loan ends will begin on that date

18. Valuation of European swaptions The valuation of European swaptions can actually be done by tweaking Black’s model for valuing futures options The swaption model relies on changing the value of the underlying, the volatility, and the discount factor The reason Black’s model benefits us in this calculation is the option contract and futures contract don’t have to mature at the same time There is also a quick way to value European swaptions that Hull and White have shown, using an analytic approach that comes up with results similar to Monte Carlo simulations for similar material

19. Valuation of Bermudan swaptions Valuation of Bermudan swaptions is usually done by using one-factor no arbitrage models that are controversial because their accuracy has been questioned Other methods include a least squares approach where the value of not exercising on a particular payment date is assumed to be a polynomial function of the values of the factors, and an optimal early exercise boundary approach Monte Carlo simulation is an important technique that can be used to value Bermudan swaptions

20. Valuation of American swaptions Valuing American swaptions is generally considered by investors to be a pain, though it is fortunate that they are not as common as European or Bermudan swaptions There is no set way to value American swaptions, although there have been certain techniques proposed including a two factor stochastic model where the factors are the short-term interest rate and the premium of the futures rate over the short-term interest rate and another model that uses trinomial trees

21. Summary A combination of extremely popular financial instruments, swaptions are popular for organizations due to the fact that they are a great way to hedge interest rate risk with a limited downside, and can be interesting speculative tools as well Because they are so complex, swaptions can be difficult to price and there is a lot of demand for quick, effective techniques to price swaption contracts that improve upon techniques that are presently used