Interest rates instruments, pricing options

The main factors determining the price of an option on an interest rate instrument such as a bond are listed below. (Their effects will differ depending on whether the option in question is a call or a put and whether it is American or European.)... 

A number of option-pricing models exist. Market participants often use variations on these models that they developed themselves or that were developed by their firms. The best-known of the pricing models is probably the Black-Scholes, whose fundamental principle is that a synthetic option can be created and valued by taking a position in the underlying asset and borrowing or lending funds in the market at the risk-free rate of interest. Although Black-Scholes is the basis for many other option models and is still used widely in the market, it is not necessarily appropriate for some interest rate instruments. Fabozzi (1997), for instance, states that the Black-Scholes model s assumptions make it unsuitable for certain bond options. As a result a number of alternatives have been developed to analyze callable bonds. 

In debt capital markets the yield on a domestic government T-bill is usually considered to represent the risk-free interest rate, since it is a shortterm instrument guaranteed by the government. This makes the T-bill rate, in theory at least, the most secure investment in the market. It is common to see the 3-month T-bill rate used in corporate finance analysis and option pricing analysis, which often refer to a risk-free money market rate. 

The pricing of other interest rate products, both cash and derivatives, that was described in previous chapters used rigid mathematical principles. This was possible because what happens to these instruments at maturity is known, allowing their fair values to be calculated. With options, however, the outcome at expiry is uncertain, since they may or may not be exercised. This uncertainty about final outcomes makes options more difficult to price than other financial market instruments. 

In 1976 Fisher Black presented a slightly modified version of the B-S model, using similar assumptions, for pricing forward contracts and interest rate options. Banks today employ this modified version, the Black model, to price swaptions and similar instruments in addition to bond and interest rate options, such as caps and floors. The bond options described in this section are options on bond futures contracts, just as the interest rate options are options on interest rate futures. 

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