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

Hi Jun Choe, Jeong Ho Chu, Jongeun Kim

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1241-1261
Number of pages21
JournalBulletin of the Korean Mathematical Society
Volume55
Issue number4
DOIs
Publication statusPublished - 2018 Jan 1

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Geometric Brownian Motion
Sample Path
Fractional Brownian Motion
Malliavin Derivative
Wick Product
Financial Derivatives
Hurst Parameter
Malliavin Calculus
Discrete-time Model
Option Pricing
Discrete Equations
Term
Strong Convergence
Convergence Analysis
Pricing
Convert
Stochastic Equations
Convergence Rate
Monte Carlo Simulation
Numerical Experiment

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Generating sample paths and their convergence of the geometric fractional brownian motion. / Choe, Hi Jun; Chu, Jeong Ho; Kim, Jongeun.

In: Bulletin of the Korean Mathematical Society, Vol. 55, No. 4, 01.01.2018, p. 1241-1261.

Research output: Contribution to journalArticle

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