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

Jiling Cao, Jeong-Hoon Kim, Xi Li and Wenjun Zhang

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 660-676

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.

Keywords: Asymptotic approximation; Barrier; Down-and-out; Floating strike; Lookback; Mellin transform; Stochastic volatility (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:660-676

DOI: 10.1016/j.matcom.2023.01.035

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