Implied Volatility of Interest Rate Options: An Empirical Application of the Market Model

Abstract

In this paper we analyze the empirical properties of the volatility implied in options on the 13-week US Treasury bill using both ITM, ATM, and OTM options. This market has not been studied previously. Moreover, these options are interesting because they are identical to options written on zero-coupon bonds which are the simplest interest rate derivate contracts possible. We apply the market model and adapt it to our data by assuming that the 13-week Treasury bill forward rate is log-normally distributed. The use of the market model separates our work from the vast majority of previous studies of implied volatility of interest rate options. We suggest three different volatility specifications: constant, affine, and exponential volatility and run a horse race between them. We document that the constant volatility specification is preferred with respect to parameter stability and the size of the average pricing errors which are rather large, -139% to -87%. Furthermore, we find that the implied volatility of yesterday contains information of the future volatility of the forward interest rates for all three volatility specifications. Finally, we show that moneyness and option type (call/put) explain 28-36% of the pricing errors. Hence, we give a partial explanation of why the market model fails.