François-Heude, Alain and Yousfi, Ouidad (2013): A Generalization of Gray and Whaley's Option.
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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.
Item Type: | MPRA Paper |
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Original Title: | A Generalization of Gray and Whaley's Option |
English Title: | A Generalization of Gray and Whaley's Option |
Language: | English |
Keywords: | strike reset, at-the-money option, liquidity, reset option. |
Subjects: | G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing |
Item ID: | 47908 |
Depositing User: | Ouidad YOUSFI |
Date Deposited: | 30 Jun 2013 18:03 |
Last Modified: | 06 Oct 2019 16:58 |
References: | Black, F. and M. Scholes, 1973, "The pricing of options and corporate liabilities", Journal of political Economics, Vol. 81, pp. 637-659. Chen J.Y., and J.Y. Wang, 2008, "The valuation of Forward-start Rainbow options", online http://69.175.2.130/~finman/Turin/Papers/The_Valuation_of_Forward_Start_Rainbow_Options.pdf. Cheng, W.Y. and S. Zhang, 2000, "The analytics of reset options", Journal of derivatives, Vol. 8, pp. 59-71. Cox, J.C., S. Ross and M. Rubinstein, 1979, "Option pricing: A simplified Approach", Journal of Financial Economics, Vol: 7, pp. 229-264. Gray, S.F. and R.E. Whaley, 1999, "Reset Put Options: Valuation, Risk Charactheristics, and an Application", Australian Journal of Management, Vol. 24, n° 1, pp. 1-20. Guo, J.H. and M.W. Hung, 2008, "A generalization of Rubinstein's Pay Now, Choose Later", Journal of Futures Markets, Vol. 28, n° 5, pp. 488--515. Haug, E. and J. Haug, 2001, "Resetting Strikes, barriers and time", The collector: Who's on first base?, Wilmott Magazine, http://www.wilmott.com/pdfs/010721_collector_02.pdf. Johnson, H., 1987, "Options on the maximum or the minimum of several assets", Journal of Financial and Quantitatives Analysis, Vol. 22, pp. 277-283. Kargin, V., 2005, "Lattice Option Pricing by Multidimensional Interpolation", Mathematical Finance, Vol. 15, No. 4, pp. 635-647. Liao, S.L. and C.W. Wang, 2003, "The valuation of reset options with multiple strike resets and reset dates", Journal of Futures Markets, Vol. 23, pp. 87-107. Merton, R. C., 1973, "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science, Vol. 4, pp. 141--183. Margrabe, W., 1978, "The value of an option to exchange one asset for another", Journal of Finance, Vol. 33, pp. 177-186. Rubinstein, M., 1991, "Pay now, choose late", Risk, Vol. 4, p.13. Stultz, R., 1991, "Options on the minimum or the maximum of two risky assets: analysis and applications", Journal of Financial Economics, Vol. 10, pp. 161-185. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/47908 |
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