Generating sample paths and their convergence of the geometric fractional brownian motion

Hi Jun Choe; Jeong Ho Chu; Jongeun Kim

doi:10.4134/BKMS.b170719

Generating sample paths and their convergence of the geometric fractional brownian motion

Hi Jun Choe, Jeong Ho Chu, Jongeun Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1241-1261
Number of pages	21
Journal	Bulletin of the Korean Mathematical Society
Volume	55
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.b170719
Publication status	Published - 2018

Bibliographical note

Funding 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.

Publisher Copyright:
©2018 Korean Mathematial Soiety.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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title = "Generating sample paths and their convergence of the geometric fractional brownian motion",

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.",

author = "Choe, {Hi Jun} and Chu, {Jeong Ho} and Jongeun Kim",

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doi = "10.4134/BKMS.b170719",

language = "English",

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AU - Chu, Jeong Ho

AU - Kim, Jongeun

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PY - 2018

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N2 - 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.

AB - 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.

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Generating sample paths and their convergence of the geometric fractional brownian motion

Abstract

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