Asset prices risk-free interest rate

The volatility of the underlying asset s price returns The risk-free interest rate applicable to the life of the option... 

As noted in Chapter 8, the value of an option is a function of five factors The price of the underlying asset The options strike price The options time to expiry The volatility of the underlying assets price returns The risk-free interest rate applicable to the life of the option... 

When valuing an option written on say, an equity the price of the underlying asset is the current price of the equity. When pricing an interest-rate option the underlying is obtained via a random process that described the instantaneous risk-free zero-coupon rate, which is generally termed the short rate. 

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. 

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