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Introduction to Pricing Approach

A swaption provides the holder with the right, but not the obligation, to enter into a specific swap deal on a future date (or set of dates). As such, swaptions provide an alternative to forward swaps in the same way that currency options provide an alternative to forward FX deals. While the forward swap does not involve any up-front cost, it does obligate the counterparty to enter the swap agreement even when it turns out that the counterparty would be worse off by doing so. Swaptions on the other hand require the payment of an initial premium but give the holder discretion as to whether the option will be exercised.

To see the benefit of the flexibility provided by a swaption, consider the situation faced by company A that needs to borrow $10M at LIBOR plus 100 basis points in six months time and intends to enter into a swap agreement at that time to effectively convert the floating rate loan into a fixed loan. The uncertainty that faces company A is that they do not know what the appropriate fixed rate for the swap will be when the deal is eventually made. The effective funding cost is therefore also uncertain and will remain so until the swap is entered in six months time.

One way to eliminate this uncertainty is to purchase an appropriately structured swaption. Lets say that company A could enter into a swaption agreement that gives them the right to receive LIBOR and pay a fixed rate of 7.5% starting in six months time. If the swap rate in six months time turns out to be greater than 7.5%, then company A would be best suited by exercising their option to enter into a swap where they are only required to pay 7.5%. Conversely, if the market swap rate turns out to be lower than 7.5%, then company A should allow the swaption to expire and simply enter into a swap at the lower fixed rate. Either way, the fixed rate of the desired swap is guaranteed to be no higher than 7.5% and company A are therefore assured that the net funding cost of the proposed loan will not exceed 8.5%.

The reduction in uncertainty that is associated with the swaption has value to company A, and a range of option pricing models can be used to estimate an exact swaption premium. However, before we consider a mathematical representation of the model, we might note that the value of the swaption to company A will be higher when:

1.

the fixed rate of the swap prescribed by the swaption contract is substantially lower than the fixed rate that is currently expected to prevail in the market at the time the swaption will expire. This will allow company A to pay a lower fixed rate than the likely prevailing market rate when the swap is initiated, and is obviously valuable from company A's point of view. In standard option pricing terms, this is a situation where a call option is well in the money

2.

the uncertainty surrounding the fixed rate that will prevail in the market when the swaption matures is greater. The greater the uncertainty, the higher the value of an instrument that is structured to eliminate that uncertainty. Like standard options, this factor is simply reflecting the positive relationship between the option value and the volatility of the underlying asset.

 

For valuation purposes, we also need to distinguish between the two broad types of interest rate swaptions. An option that gives the right to pay fixed and receive floating is called a payer swaption, while those that give the right to receive fixed and pay floating are described as receiver swaptions. In general option pricing terms, the former swaption type can be thought of as a call option, and the receiver swaption treated as a put option.

In This Section

European Swaptions

American and Bermudan Swaptions

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