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What is Learnable in Valiant's Theory of the Learnable? 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A Delayed Black and Scholes Formula I
Mercedes Arriojas, Yaozhong Hu, Salah-Eldin Mohammed, Gyula Pap · 2006-04-29 · via math.ST updates on arXiv.org

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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