A Delayed Black and Scholes Formula I

Details A Delayed Black and Scholes Formula I A Delayed Black and Scholes Formula I

2006-04-28

arxiv.org/abs/math/0604640v1

Mathematics

Probability

Scientific paper

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure.

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