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The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps. (English) Zbl 1092.91020

The authors derive the density process of the minimal entropy martingale measure in a stochastic volatility model proposed by O. E. Barndorff-Nielsen and N. Shephard [J. R. Stat. Soc., Ser. B, Stat. Methodol. 63, No. 2, 167–241 (2001; Zbl 0983.60028)]. These results are applied to find the minimal entropy price of derivatives in the market. A system of integro-partial differential equations that determines the price is presented. The price is written as an expected value of the payoff which gives the complete knowledge of the dynamics of the asset and volatility processes. The integro-PDE for the pricing equation is stated which will become a Black-Scholes PDE with an additional integral term arising from the jumps in the stochastic volatility.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60G51 Processes with independent increments; Lévy processes
60G57 Random measures
60H30 Applications of stochastic analysis (to PDEs, etc.)

Citations:

Zbl 0983.60028
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