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Increasing The Accuracy Of Option Pricing By Using Implied Parameters Related To Higher Moments

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  • Ji, Dasheng
  • Brorsen, B. Wade

Abstract

The inaccuracy of the Black-Scholes formula arises from two aspects: the formula is for European options while most real option contracts are American; the formula is based on the assumption that underlying asset prices follow a lognormal distribution while in the real world asset prices cannot be described well by a lognormal distribution. We develop an American option pricing model that allows non-normality. The theoretical basis of the model is Gaussian quadrature and dynamic programming. The usual binomial and trinomial models are special cases. We use the Jarrow-Rudd formula and the relaxed binomial and trinomial tree models to imply the parameters related to the higher moments. The results demonstrate that using implied parameters related to the higher moments is more accurate than the restricted binomial and trinomial models that are commonly used.

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Bibliographic Info

Paper provided by NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management in its series 2000 Conference, April 17-18 2000, Chicago, Illinois with number 18945.

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Date of creation: 2000
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Handle: RePEc:ags:ncrtci:18945

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Web page: http://www.agebb.missouri.edu/ncrext/ncr134/

Related research

Keywords: option pricing; volatility smile; Edgeworth series; Gaussian Quadrature; relaxed binomial and trinomial tree models; Marketing; Risk and Uncertainty;

References

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  1. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
  2. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  3. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
  4. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  5. 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 637-54, May-June.
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