On the calculation of price sensitivities with jump-diffusion structure
We provide a new theoretical framework for estimating the price sensitivities of a trading position with regard to five underlying factors in jump-diffusion models using jump times Poisson noise. The proposition that results in a general solution is mathematically proved. The general solution that this paper offers can be applied to compute each price sensitivity. The suggested modeling approach deals with the shortcomings of the Black-Scholes formula such as the jumps that can occur at any time in the stock's price. Via the Malliavin calculus we show that differentiation can be transformed into integration, which makes the price sensitivities operational and more efficient. Thus, the solution that is provided in this paper is expected to make decision making under uncertainty more efficient.
|Date of creation:||2011|
|Date of revision:|
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- Kawai, Reiichiro & Takeuchi, Atsushi, 2010. "Sensitivity analysis for averaged asset price dynamics with gamma processes," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 42-49, January.
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- Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, 05.
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