OPTION PRICING FOR INCOMPLETE MARKETS VIA STOCHASTIC OPTIMIZATION: TRANSACTION COSTS, ADAPTIVE CONTROL AND FORECAST

Sergei Fedotov () and Sergei Mikhailov ()
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Sergei Fedotov: Mathematics Department, UMIST, Manchester M60 1QD, UK
Sergei Mikhailov: University of Wuppertal, D-42097 Wuppertal, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 01, 179-195

Abstract: The problem of determining the European-style option price in incomplete markets is examined within the framework of stochastic optimization. An analytic method based on the stochastic optimization is developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal feedback control) that reduces the total risk inherent in writing the option. The cases involving transaction costs, the stochastic volatility with uncertainty, stochastic adaptive process, and forecasting process are considered. A software package for the option pricing for incomplete markets is developed and the results of numerical simulations are presented.

Keywords: Option pricing; incomplete markets; stochastic optimization; transaction costs; adaptive control; forecast (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024901000912

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