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

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Listed:
  • Cao, Jiling
  • Kim, Jeong-Hoon
  • Li, Xi
  • Zhang, Wenjun

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.

Suggested Citation

  • Cao, Jiling & Kim, Jeong-Hoon & Li, Xi & Zhang, Wenjun, 2023. "Valuation of barrier and lookback options under hybrid CEV and stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 660-676.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:660-676
    DOI: 10.1016/j.matcom.2023.01.035
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    References listed on IDEAS

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