## Option pricing when underlying stock returns are discontinuous (1976)

Venue: | Journal of Financial Economics |

Citations: | 505 - 1 self |

### BibTeX

@ARTICLE{Merton76optionpricing,

author = {Robert C. Merton},

title = {Option pricing when underlying stock returns are discontinuous},

journal = {Journal of Financial Economics},

year = {1976},

volume = {3},

pages = {125--144}

}

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### Abstract

The validity of the classic Black-Scholes option pricing formula dcpcnds 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 cast when the underlying stock returns are gcncrated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black&holes formula in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to the pricingofcorporatc liabilities. 1. Intruduction In their classic paper on the theory of option pricing, Black and Scholcs (1973) prcscnt a mode of an:llysis that has rcvolutionizcd the theory of corporate liability pricing. In part, their approach was a breakthrough because it leads to pricing formulas using. for the most part, only obscrvablc variables. In particular,