A Path-Independent Humped Volatility Model for Option Pricing

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, <italic>Econometrica</italic>, 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, <italic>Review of Derivatives Research</italic>, 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, <italic>Review of Derivatives Research</italic>, 3(3), pp. 237--262) model.