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

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. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.