A Delayed Black and Scholes Formula

Arriojas, Mercedes and Hu, Yaozhong and Mohammed, Salah-Eldin and Pap, Gyula (2007) A Delayed Black and Scholes Formula. Stochastic Analysis and Applications, 25 (2). pp. 471-492. ISSN 0736-2994

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Abstract

In this article we develop an explicit formula for pricing European options when the underlying stock price follows nonlinear stochastic functional differential equations with fixed and variable delays. We believe that the proposed models are sufficiently flexible to fit real market data, and yet simple enough to allow for a closed-form representation of the option price. Furthermore, the models maintain the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent local martingale measure.

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