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Asian option pricing with transaction costs and dividends under the fractional Brownian motion model. (English) Zbl 1406.91460

Summary: The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. Then by solving the partial differential equation, the pricing formula and call-put parity of the geometric average Asian option with dividend payment and transaction costs are obtained. At last, the influences of Hurst index and maturity on option value are discussed by numerical examples.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
60G22 Fractional processes, including fractional Brownian motion
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