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Pricing foreign equity options under Lévy processes

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  • Shian‐Chang Huang
  • Mao‐Wei Hung

Abstract

This article investigates the valuation of a foreign equity option whose value depends on the exchange rate and foreign equity prices. Assuming that these underlying price processes are correlated and driven by a multidimensional Lèvy process, a method suitable for solving the complex valuation problem is developed. First, to reduce the number of dimensions of the problem, the probability measure is changed to embed some dimensions of the Lèvy process into the pricing measure. Second, to simplify the integral complexity of the discounted terminal payoff, the valuation problem is transformed to Fourier space. The main contribution of this study is that by combining these two methods, the multivariate valuation problem is significantly simplified, and very accurate results are obtained relatively quickly. This powerful method can also be applied to other multivariate pricing problems involving Lèvy processes. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:917–944, 2005

Suggested Citation

  • Shian‐Chang Huang & Mao‐Wei Hung, 2005. "Pricing foreign equity options under Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(10), pages 917-944, October.
    • Handle: RePEc:wly:jfutmk:v:25:y:2005:i:10:p:917-944
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    Cited by:

    1. Ma, Yong & Pan, Dongtao & Shrestha, Keshab & Xu, Weidong, 2020. "Pricing and hedging foreign equity options under Hawkes jump–diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Ulyah, Siti Maghfirotul & Lin, Xenos Chang-Shuo & Miao, Daniel Wei-Chung, 2018. "Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps," Finance Research Letters, Elsevier, vol. 24(C), pages 113-128.
    3. Mozumder, Sharif & Dempsey, Michael & Kabir, M. Humayun & Choudhry, Taufiq, 2016. "An improved framework for approximating option prices with application to option portfolio hedging," Economic Modelling, Elsevier, vol. 59(C), pages 285-296.
    4. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2024. "Pricing derivatives on foreign assets using Markov-modulated cojump-diffusion dynamics," International Review of Economics & Finance, Elsevier, vol. 93(PB), pages 503-519.
    5. Li, Shaoyu & Huang, Henry H. & Zhang, Teng, 2020. "Generalized affine transform on pricing quanto range accrual note," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    6. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    7. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    8. Wei Wang & Qianyan Li & Quan Li & Song Xu, 2023. "Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    9. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.

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