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Path-dependent option valuation when the underlying path is discontinuous

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  • Chunsheng Zhou

Abstract

The payoffs of path-dependent options depend not only on the final values, but also on the sample paths of the prices of the underlying assets. A rigorous modeling of the underlying asset price processes which can appropriately describe the sample paths is therefore critical for pricing path-dependent options. This paper allows for discontinuities in the sample paths of the underlying asset prices by assuming that these prices follow jump diffusion processes. A general yet tractable approach is presented to value a variety of path-dependent options with discontinuous processes. The numerical examples show that ignoring the jump risk may lead to serious biases in path-dependent option pricing.

Suggested Citation

  • Chunsheng Zhou, 1997. "Path-dependent option valuation when the underlying path is discontinuous," Finance and Economics Discussion Series 1997-16, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:1997-16
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    References listed on IDEAS

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    1. Kon, Stanley J, 1984. " Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    4. Merton, Robert C, 1976. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, American Finance Association, vol. 31(2), pages 333-350, May.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    Keywords

    Asset-backed financing ; Options (Finance);

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