Pricing Derivatives the Martingale Way

Pierre Collin Dufresne William Keirstead and Michael P. Ross.

No RPF-279, Research Program in Finance Working Papers from University of California at Berkeley

Abstract: In recent years results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we show how efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multi-dimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until now have mostly been used for purely theoretical purposes.

Date: 1998-07-01
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