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A Generalization of Gray and Whaley's Option

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  • François-Heude, Alain
  • Yousfi, Ouidad

Abstract

Options markets display interesting features. Most options are executed when they are near the money. However, the underlying asset price varies significantly during the life-time option. It is therefore difficult to predict the future option position. In order to make options' markets more liquid, the paper proposes to replace all options into At-the-Money (ATM) ones by resetting the strike price X to the asset price at pre-specified time point t, before maturity time T. Strike price is locked in at the then underlying asset price S_{t} regardless whether it is above or below S_{t}.The reset condition is in exchange for deposit in the Clearing House. The idea is to provide a general valuation of reset option of Gray and Whaley (1999) in which reset condition does not depend on the relation between the strike price and the underlying asset price. The contribution of this paper is double. First, it shows that our general model option, under specific conditions, can be generalized to the most common ones like for example Black-Scholes-Merton, forward-start and strike reset pricing formulae etc... Second, in line with Haug and Haug (2001), we use the CRR binominal approach (Cox et al., 1979) and an estimation program of the cumulative bivariate normal distribution to provide closed-form solution for the pricing of the generalized European reset option.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47908.

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Date of creation: 30 Jun 2013
Date of revision: 30 Jun 2013
Handle: RePEc:pra:mprapa:47908

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Keywords: strike reset; at-the-money option; liquidity; reset option.;

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References

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  1. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
  2. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, American Finance Association, vol. 33(1), pages 177-86, March.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance, EconWPA 0309003, EconWPA, revised 29 Oct 2004.
  5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  6. Stephen F. Gray & Robert E. Whaley, 1999. "Reset Put Options: Valuation, Risk Characteristics, and an Application," Australian Journal of Management, Australian School of Business, Australian School of Business, vol. 24(1), pages 1-20, June.
  7. Johnson, Herb, 1987. "Options on the Maximum or the Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 22(03), pages 277-283, September.
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Cited by:
  1. François-Heude, Alain & Yousfi, Ouidad, 2013. "On the liquidity of CAC 40 index options Market," MPRA Paper 47921, University Library of Munich, Germany, revised 01 Jul 2013.

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