TAILIEUCHUNG - OPTION PRICING WHEN UNDERLYING STOCK RETURNS ARE DISCONTINUOUS*

A put option contract gives its holder the right to sell a specified number of shares of the underlying stock at the given strike price on or before the expiration date of the contract. I. Buying puts to participate in downward price movements. Put options may provide a more attractive method than shorting stock for profiting on stock price declines, in that, with purchased puts, you have a known and predetermined risk. The most you can lose is the cost of the option. If you short stock, the potential loss, in the event of a price upturn, is unlimited. Another advantage of buying puts results from your paying. | Journal of Financial Economics 3 1976 125-144. Nonh-Holland Publishing Company OPTION PRICING WHEN UNDERLYING STOCK RETURNS ARE DISCONTINUOUS Robert c. MERTON Massachusetts Institute of Technology Cambridge Mass. 02139 . Received May 1975 revised version received July 1975 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. 1. Introduction In their classic paper on the theory of option pricing. Black and Scholes 1973 present a mode of analysis that has revolutionized 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 observable variables. In particular their formulas do not require knowledge of cither investors tastes or their beliefs about expected returns on the underlying common stock. Moreover under specific posited conditions their formula must hold to avoid the creation of arbitrage possibilities. To derive the option pricing formula. Black and Scholes2 assume ideal conditions in the market for the stock and option. These conditions are An earlier version of this paper with the same title appeared as a Sloan School of Management Working .

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