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.
Bibliographical noteFunding Information:
Received August 14, 2017; Accepted November 3, 2017. 2010 Mathematics Subject Classification. Primary 60G22. Key words and phrases. discrete asset model, Monte Carlo, geometric fractional Brownian motion, Malliavin calculus, Euler-Maruyama scheme, Black-Scholes model. This work was supported by NRF under grant 2015R1A5A1009350.
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