### Abstract

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 language | English |
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Pages (from-to) | 2209-2223 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 64 |

Issue number | 7 |

DOIs | |

Publication status | Published - Oct 2012 |

### Fingerprint

### Keywords

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

### Cite this

}

*Computers and Mathematics with Applications*, vol. 64, no. 7, pp. 2209-2223. https://doi.org/10.1016/j.camwa.2012.01.037

**The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model.** / Baduraliya, Chaminda; Mao, Xuerong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model

AU - Baduraliya, Chaminda

AU - Mao, Xuerong

PY - 2012/10

Y1 - 2012/10

N2 - 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 modeldV(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.

AB - 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 modeldV(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.

KW - Euler-Maruyama method

KW - stochastic differential equation

KW - Brownian motion

KW - option value

UR - http://www.scopus.com/inward/record.url?scp=84866060354&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2012.01.037

DO - 10.1016/j.camwa.2012.01.037

M3 - Article

VL - 64

SP - 2209

EP - 2223

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 7

ER -