Non-Parametric Pricing of Interest Rates Options

Abstract

The pricing models for interest rates derivatives largely used today employ, many times,excessively restrictive premises in regards to the underlying assets' volatility. The Black and Scholes and the Vasicek methods, for example, consider the variance of the series as constant in time and among different maturities, assumption that may not be the

most adequate in all cases. In this paper we discuss the non-parametric estimation of the volatility function using a kernel regression technique and later the pricing of options in a Gaussian HJM model. We analyzed different possible specifications for the non-parametric estimation using the Monte Carlo simulations to price options on zero coupon bonds. We also carried out an empirical study using the proposed methodology

for the pricing of IDI Index options in the Brazilian market.