Generating sample paths and their convergence of the geometric fractional Brownian motion
Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1241-1261
https://doi.org/10.4134/BKMS.b170719
Published online July 31, 2018
Hi Jun Choe, Jeong Ho Chu, Jongeun Kim
Yonsei University, Yuanta Securities Korea, Yonsei University
Abstract : We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial deri\-vatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order $H$ which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.
Keywords : discrete asset model, Monte Carlo, geometric fractional Brownian motion, Malliavin calculus, Euler-Maruyama scheme, Black-Scholes model
MSC numbers : Primary 60G22
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