A Path-Independent Humped Volatility Model for Option Pricing

Abstract

This article presents a path-independent model for evaluating interest-sensitive claims in a Heath–Jarrow–Morton (1992, Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica, 60, pp. 77–105) framework, when the volatility structure of forward rates shows the deterministic and stationary humped shape analysed by Ritchken and Chuang (2000, Interest rate option pricing with volatility humps, Review of Derivatives Research, 3(3), pp. 237–262). In our analysis, the evolution of the term structure is captured by a one-factor short rate process with drift depending on a three-dimensional state variable Markov process. We develop a lattice to discretize the dynamics of each variable appearing in the short rate process, and establish a three-variate reconnecting tree to compute interest-sensitive claim prices. The proposed approach makes the evaluation problem path-independent, thus overcoming the computational difficulties in managing path-dependent variables as it happens in the Ritchken–Chuang (2000, Interest rate option pricing with volatility humps, Review of Derivatives Research, 3(3), pp. 237–262) model.