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The valuation of European option under subdiffusive fractional Brownian motion of the short rate. (English) Zbl 1447.91184

Summary: In this paper, we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze European option in a fractional Black-Scholes environment, when the short rate follows the subdiffusive fractional Black-Scholes model. We derive a pricing formula for call and put options and discuss the corresponding fractional Black-Scholes equation. We present some features of our model pricing model for the cases of \(\alpha\) and \(H\).

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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