Advances and Applications in Statistics
Volume 16, Issue 1, Pages 25 - 47
(May 2010)
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A GEOMETRIC BROWNIAN MOTION MODEL WITH COMPOUND POISSON PROCESS AND FRACTIONAL STOCHASTIC VOLATILITY
A. Intarasit and P. Sattayatham
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Abstract: In this paper, we introduce an approximate approach to a geometric Brownian motion (gBm) model with compound Poisson processes and fractional stochastic volatility. Based on a fundamental result on the ‑approximation of this fractional noise by semimartingales, we prove a convergence theorem concerning an approximate solution. A simulation example shows a significant reduction of error in a gBm with jump and fractional stochastic volatility as compared to the stochastic volatility. |
Keywords and phrases: geometric Brownian motion, compound Poisson process, fractional stochastic volatility, approximate models. |
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