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http://dx.doi.org/10.4134/BKMS.b170719

GENERATING SAMPLE PATHS AND THEIR CONVERGENCE OF THE GEOMETRIC FRACTIONAL BROWNIAN MOTION  

Choe, Hi Jun (Department of Mathematics Yonsei University)
Chu, Jeong Ho (Yuanta Securities Korea Bldg)
Kim, Jongeun (Department of Mathematics Yonsei University)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.4, 2018 , pp. 1241-1261 More about this Journal
Abstract
We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives 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;
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