swap tions

8/6/2019 Swap Tions

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Chris Dzera

8/6/2019 Swap Tions


�Discuss building blocks of swaptions,including some we have discussed in classand 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

8/6/2019 Swap Tions


� A n 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 thelargest derivatives market in the world

8/6/2019 Swap Tions


� 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 wheninvestors want to speculate about a

certain value

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�The most common type of swap and themost common type of interest ratederivative is a ´vanillaµ interest rate swap

�

Typically the floating rate in interest rateswap agreements is a fixed rate such as theLondon Interbank Offered Rate (LIBOR)

�These swaps usually involve fixed ratesbeing swapped for floating rates, but there

are many variations� Interest rate swaps allow for hedging of

assets and liabilities, as well as speculationby investors

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� A n 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

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� A swaption is an option on a swap contract, typicallyand almost exclusively an interest rate swap

� The first swaption contract was constructed andexecuted by William Lawton in 1983

� The contract was for a period of one year, and hiscompany sold the right to enter a five year interestrate swap to pay fixed versus 3-month LIBOR on anotional amount of $5 million at a premium

� Like the building block derivatives discussed earlierswaptions are very popular because they can beused to hedge and they also allow for speculation

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�Premium

�Strike rate (also fixed rate of underlying

swap)�Length of option period

�Length of underlying swap

�Notional amount

� A mortization, if any�Frequency of settlement of payments on

the underlying swap

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�Two parties agree to the previouslymentioned components

�The contract holder decides at some date

(or multiple dates, depending on thestructure of the contract) whether or notthey would like to enter the contract beforethe 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 onlyexchange of payments is the premium

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�Payer swaption ² gives the owner of the

swaption the right to enter a swap

contract where they pay thef ixed legand receive the floating leg

�Receiver swaption ² gives the owner of

the swaption the right to enter into a

swap contract where they pay thefloating leg and receive the f ixed leg

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� There are three different ways the right toexercise the option in a swaption contract can bescheduled

� European

² the owner of the contract canexercise his right to enter the swap at maturity

� American ² the owner of the contract canexercise his right to enter the swap at any datebetween the start and end dates of the option

period agreed to� Bermudan ² the owner of the contract can

exercise his right to enter the swap at certainpredetermined dates between the start and end

dates of the option period

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�There are two types of A merican swaptions:� A n A merican swaption with f ixed 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, aslong as it is exercised before the option periodexpires

� A n A merican swaption with f ixed end date is whenthe predetermined period of time includes the

length of the option period and the underlying swap,so if the day the swap would begin passes withoutthe swap being exercised, the length of theunderlying swap decreases

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�Because the option period can end beforethe swap takes place, it may be unclear whyit is logical to pay a premium for the option

to enter a swap contract down the road when the party could just decide whether ornot they want to enter the contract at thatlater date

�However, entering a swaption contractassures that the party that holds the contracthas the option to receive better terms on theswap contract than they would have if they

had waited

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� A company knows that in two years it willhave to enter a 5 year loan on $5 million

with a 2% interest rate, and wants to

reduce its interest rate risk byexchanging its payments on this contractfor floating payments

�They enter a swaption contract with a 2year option period, where at the end of 2years on the expiry date of the option, if they exercise the option a 5 year swap

would be initiated

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� A bond holder knows that in one year they will receive fixed rates of 3% on $2 millionbond for a period of ten years, and wants to

receive a floating rate instead�They enter a swaption contract that expiresin one year with specific exercise datesafterward that would not go too far into theswap period

� If they elected to exercise after expiry, thelength of the swap would be reduced by theamount of time between the end of theoption period and the date the option wasexercised

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� 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 anytime in the option period, a 13 year swap

with terms agreed to begins immediately

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� 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, aswap that ends when the loan ends will

begin on that date

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� The valuation of European swaptions can actuallybe done by tweaking Black·s model for valuingfutures options

� The swaption model relies on changing the value

of the underlying, the volatility, and the discountfactor

� The reason Black·s model benefits us in thiscalculation is the option contract and futurescontract don·t have to mature at the same time

� There is also a quick way to value Europeanswaptions that Hull and White have shown, usingan analytic approach that comes up with resultssimilar to Monte Carlo simulations for similarmaterial

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� Valuation of Bermudan swaptions is usually doneby using one-factor no arbitrage models that arecontroversial because their accuracy has been

questioned� Other methods include a least squares approach

where the value of not exercising on a particularpayment date is assumed to be a polynomialfunction 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 Bermudanswaptions

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� Valuing A merican swaptions is generallyconsidered by investors to be a pain, thoughit is fortunate that they are not as common as

European or Bermudan swaptions�There is no set way to value A mericanswaptions, although there have been certaintechniques proposed including a two factorstochastic model where the factors are the

short-term interest rate and the premium of the futures rate over the short-term interestrate and another model that uses trinomialtrees

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� A combination of extremely popularfinancial instruments, swaptions are popularfor organizations due to the fact that they

are a great way to hedge interest rate risk with a limited downside, and can beinteresting speculative tools as well

�Because they are so complex, swaptions canbe difficult to price and there is a lot of

demand for quick, effective techniques toprice swaption contracts that improve upontechniques that are presently used

swap tions

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