A Path-Independent Humped Volatility Model for Option Pricing

This article presents a path-independent model for evaluating interest-sensitiveclaims 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 shapeanalysed by Ritchken and Chuang (2000, Interest rate option pricing with volatility humps, Reviewof Derivatives Research, 3(3), pp. 237–262). In our analysis, the evolution of the term structure iscaptured by a one-factor short rate process with drift depending on a three-dimensional state variableMarkov process. We develop a lattice to discretize the dynamics of each variable appearing inthe short rate process, and establish a three-variate reconnecting tree to compute interest-sensitiveclaim prices. The proposed approach makes the evaluation problem path-independent, thus overcomingthe computational difficulties in managing path-dependent variables as it happens in theRitchken–Chuang (2000, Interest rate option pricing with volatility humps, Review of DerivativesResearch, 3(3), pp. 237–262) model.