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Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump‐Diffusion Models

Author

Listed:
  • Kaili Xiang
  • Yindong Zhang
  • Xiaotong Mao

Abstract

Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that the exchange rate follows the extended Vasicek model, we obtain the closed form of the pricing formulas for two kinds of power options under fractional Brownian Motion (FBM) jump‐diffusion models.

Suggested Citation

  • Kaili Xiang & Yindong Zhang & Xiaotong Mao, 2014. "Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump‐Diffusion Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:259297
    DOI: 10.1155/2014/259297
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    References listed on IDEAS

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    1. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    2. Robert Elliott & Leunglung Chan, 2004. "Perpetual American options with fractional Brownian motion," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 123-128.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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