A Generalization of Gray and Whaley's Option

19 Pages Posted: 30 Jun 2013

See all articles by Alain François Heude

Alain François Heude

Université Montpellier II - Montpellier Research in Management (MRM)

Ouidad Yousfi

Université de Montpellier

Date Written: June 30, 2013

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.

Suggested Citation

François Heude, Alain and Yousfi, Ouidad, A Generalization of Gray and Whaley's Option (June 30, 2013). Available at SSRN: https://ssrn.com/abstract=2287423 or http://dx.doi.org/10.2139/ssrn.2287423

Alain François Heude

Université Montpellier II - Montpellier Research in Management (MRM) ( email )

Place Eugène Bataillon
Montpellier, 34095
France

Ouidad Yousfi (Contact Author)

Université de Montpellier ( email )

Place Eugène Bataillon
Montpellier, 34095
France

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