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Exchange option pricing in jump-diffusion models based on esscher transform

Author

Listed:
  • Wenhan Li
  • Lixia Liu
  • Guiwen Lv
  • Cuixiang Li

Abstract

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Esscher transform parameters, we obtain a risk-neural measure Q under which the discounted value of the risky underlying asset is a martingale. Then, we give the pricing formulas of Exchange option by change of numeraire. At last, we analyze the option pricing formula and provide numerical illustrations by introducing BBY stock and SBUX stock.

Suggested Citation

  • Wenhan Li & Lixia Liu & Guiwen Lv & Cuixiang Li, 2018. "Exchange option pricing in jump-diffusion models based on esscher transform," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(19), pages 4661-4672, October.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:19:p:4661-4672
    DOI: 10.1080/03610926.2018.1444180
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    Cited by:

    1. Zhuoxin Liu & Laijun Zhao & Chenchen Wang & Yong Yang & Jian Xue & Xin Bo & Deqiang Li & Dengguo Liu, 2019. "An Actuarial Pricing Method for Air Quality Index Options," IJERPH, MDPI, vol. 16(24), pages 1-19, December.
    2. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "The second-order Esscher martingale densities for continuous-time market models," Papers 2407.03960, arXiv.org.
    3. Bahareh Afhami & Mohsen Rezapour & Mohsen Madadi & Vahed Maroufy, 2021. "Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk," Papers 2104.11594, arXiv.org.

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