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

  • Nguyen Thanh Long

    (Warsaw School of Economics)

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.

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Paper provided by EconWPA in its series Finance with number 0207004.

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Length: 36 pages
Date of creation: 16 Aug 2002
Date of revision: 19 Nov 2002
Handle: RePEc:wpa:wuwpfi:0207004
Note: Type of Document - TeX/PDF; prepared on PC-TEX; pages: 36
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  1. 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 327-43.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. 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.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  5. 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 727-52.
  6. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
  7. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  9. 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.
  10. 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 1209-27, July.
  11. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
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