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Asian options with jumps

Author

Listed:
  • Chou, Ching-Sung
  • Lin, Hsien-Jen

Abstract

The paper is concerned with the computation of Asian options when the underlying asset has a jump. In the Black and Scholes model, Geman and Yor give a closed-form of formula for the price of an Asian option at a random exponential distributed maturity (it then "suffices" to invert the Laplace transform to have the price at a fixed time). The aim of this paper is to obtain such a formula in a model (which seems more realistic) of Black and Scholes with a jump at a random time, which extends the well-known case of the continuous Black and Scholes model. Furthermore, we treat the multi-jump case. Here we also develop a formula for pricing such an option.

Suggested Citation

  • Chou, Ching-Sung & Lin, Hsien-Jen, 2006. "Asian options with jumps," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1983-1993, December.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:18:p:1983-1993
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    References listed on IDEAS

    as
    1. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. Protter, Philip, 2001. "A partial introduction to financial asset pricing theory," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 169-203, February.
    3. Aase, Knut K., 1988. "Contingent claims valuation when the security price is a combination of an Ito process and a random point process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 185-220, June.
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    Cited by:

    1. Chou, Ching-Sung & Lin, Hsien-Jen, 2007. "Pricing model for zero coupon bonds driven by Bessel-squared interest processes with a jump," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 475-482, March.
    2. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.

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