Interest Rate Futures Options and Interest Rate Options

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Abstract
This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage‐free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage‐free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed‐form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.

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