Pricing Eurodollar futures options using the BDT term structure model: The effect of yield curve smoothing

Headnote

This article focuses on pricing Eurodollar futures options using the single-factor Black, Derman, and Toy (1990) term structure model with particular emphasis on yield curve smoothing. Of the various approaches, the maximum smoothness forward rate approach developed by Adams and van Deventer (1994), cubic yield spline, and linear interpolation are used to produce finely spaced binomial trees. We compare the pricing accuracy associated with the use of yield curve smoothing techniques within the BDT framework. The findings provide the first supporting evidence that using a forward rate curve with maximum smoothness together with a time-varying volatility structure improves best the performance of the BDT model. The empirical results are found to be robust across factors affecting the option price such as time-to-expiration, moneyness, and trading volume. (C) 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 293-306, 2000.

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INTRODUCTION

This article provides empirical evidence on the effectiveness of forward rate curve smoothing in pricing Eurodollar futures options using the Black, Derman, and Toy (1990; henceforth BDT) term structure model. The BDT model has been popular among practitioners partly for its ease of calibration and for its straightforward solutions. The model uses two sets of inputs, a yield and volatility curve, in pricing interest rate sensitive claims. This study emphasizes that using a better representation of the yield and volatility curves can enhance the performance of the BDT model, which then yields more precise estimated option prices.

The original BDT model requires a binomial tree with finely spaced steps to obtain accurate solutions for option values.1 This can be achieved by choosing actual interest rates with the shortest-maturity increments available. Smoothing the initial yield curve to reduce the interval size can increase model accuracy even further. The article makes a contribution to the literature by providing evidence of the assertion that the use of finely spaced binomial trees in the BDT model yields more precise estimated option prices.

To price Eurodollar futures options more accurately using the BDT model, one needs to obtain rates with shorter maturities than the original interval size of three months. In the literature, yield curve smoothing is used to derive shorter maturity interest rates from the observed market data. Of the...