Full-fledged SABR through Markov Chains

Abstract

We present a general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form matrix expressions for European options are derived. We also propose a recursive risk-neutral valuation technique for pricing discretely monitored path-dependent options, and use it to price Bermudan and barrier options. In addition, we provide single Laplace transform formula for discretely monitored arithmetic Asian options. Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.

Keywords: SABR model, Markov chain, exotic options, calibration

JEL Classification: C58, G13, G17