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Analytical Aproach to Value Options with State Variables of a Levy System

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  • Nguyen Thanh Long

    (Warsaw School of Economics)

Abstract

In this paper we discuss an analytical method in pricing contingent claims of European style on the assets, whose state variables follow a multi-dimensional Levy process. We give explicit formulae for the hypothetical ``two-price'' contingent claim prices by means of the conditional characteristic transforms. The work not only unifies and extends the option pricing literature, which focuses on the use of the characteristic function, but also provides the way to formalize and unify the valuation of the contingent claim price, the valuation of the discount bond price, the valuation of the scaled-forward price, and determining the pricing measures in incomplete markets.

Suggested Citation

  • Nguyen Thanh Long, 2002. "Analytical Aproach to Value Options with State Variables of a Levy System," Finance 0207004, EconWPA, revised 19 Jan 2003.
  • Handle: RePEc:wpa:wuwpfi:0207004
    Note: Type of Document - TeX/PDF; prepared on PC-TEX; pages: 36
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    2. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31 World Scientific Publishing Co. Pte. Ltd..
    6. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Nengjiu Ju & Rui Zhong, 2006. "Fourier transformation and the pricing of average-rate derivatives," Review of Derivatives Research, Springer, vol. 9(3), pages 187-212, November.
    9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    11. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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    More about this item

    Keywords

    Levy Process; Option Pricing; Characteristic Function; Analitical Method; Fourier transform;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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