Valuation of barrier and lookback options under hybrid CEV and stochastic volatility

Abstract

In this paper, we evaluate down-and-out put option and floating strike lookback option prices when the underlying asset is driven by a hybrid model with constant elasticity of variance and stochastic volatility (SVCEV). Usually, it is difficult to get closed-form solutions for those exotic options under stochastic volatility models. Here, we use an asymptotic expansion approach and the Mellin transform method to obtain explicit closed-form formulae for the zero-order and first-order correction terms. In addition, we perform a sensitivity analysis numerically on the asymptotic terms and compare the option prices corresponding to the Black–Scholes, CEV and SVCEV models with those calculated by Monte-Carlo simulations and the binomial tree method to illustrate the accuracy of our pricing formulae.