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A Delayed Black and Scholes Formula I

Author

Listed:
  • Mercedes Arriojas
  • Yaozhong Hu
  • Salah-Eldin Mohammed
  • Gyula Pap

Abstract

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure.

Suggested Citation

  • Mercedes Arriojas & Yaozhong Hu & Salah-Eldin Mohammed & Gyula Pap, 2006. "A Delayed Black and Scholes Formula I," Papers math/0604640, arXiv.org.
    • Handle: RePEc:arx:papers:math/0604640
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    References listed on IDEAS

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    1. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    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.
    4. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    5. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    7. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
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