Generalized pricing formulas for stochastic volatility jump diffusion
models applied to the exponential Vasicek model |
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Authors: | L ZJ Liang D Lemmens and J Tempere |
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Institution: | (1) School of Business, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul, 120-749, Republic of Korea;(2) Samsung Investment Trust Management Co., Ltd, 36-1 Samsung Life Youido Bldg. Youido-dong, Youngdeungpo-gu, Seoul, 150-886, Republic of Korea;(3) Graduate School of Management, Korea Advanced Institute of Science and Technology, 207-43 Cheongyangni2-dong, Dongdaemoon-gu, Seoul, 130-722, Republic of Korea;(4) School of Management, Seoul Woman’s University, 126 Gongreung-dong, Nowon-gu, Seoul, 139-774, Republic of Korea |
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Abstract: | Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a
Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present
a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes
are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility
models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate
jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond
the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from
superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations. |
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