The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model

Chaminda Baduraliya, Xuerong Mao

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Stochastic differential equations (SDEs) have been used to model an asset price and its volatility in finance. Lewis (2000) [10] developed the mean-reverting-theta processes which can not only model the volatility but also the asset price. In this paper, we will consider the following mean-reverting-theta stochastic volatility model
dV(t)=α2(μ2−V(t))dt+σ2V(t)βdw2(t).
We will first develop a technique to prove the non-negativity of solutions to the model. We will then show that the EM numerical solutions will converge to the true solution in probability. We will also show that the EM solutions can be used to compute some financial quantities related to the SDE model including the option value, for example.
Original languageEnglish
Pages (from-to)2209-2223
Number of pages15
JournalComputers and Mathematics with Applications
Volume64
Issue number7
DOIs
Publication statusPublished - Oct 2012

Keywords

  • Euler-Maruyama method
  • stochastic differential equation
  • Brownian motion
  • option value

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