Elsevier

Journal of Financial Economics

Volume 3, Issues 1–2, January–March 1976, Pages 125-144
Journal of Financial Economics

Option pricing when underlying stock returns are discontinuous

https://doi.org/10.1016/0304-405X(76)90022-2Get rights and content

Abstract

The validity of the classic Black-Scholes option pricing formula depends on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the more-general case when the underlying stock returns are generated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black-Scholes formula in that it does not depend on investor preferences or knowledge of the expected return on the underlying stock. Moreover, the same analysis applied to the options can be extended to the pricing of corporate liabilities.

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    An earlier version of this paper with the same title appeared as a Sloan School of Management Working Paper #787-75 (April 1975). Aid from the National Science Foundation is gratefully acknowledged.

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