Efficient Monte Carlo option pricing under CEV model

ABSTRACT

One of the financial model with nonconstant volatiltiy is the constant elasticity of varinace model, or CEV model for short. The CEV model is an altrnative to the Black–Scholes model of stock price movements. In this diffusion process, unlike the Black–Scholes model, the volatility is a function of the stock price and involves two parameters. In this article, we propose an efficient Monte-Carlo algorithm for pricing arithmetic Asian option under CEV model. In an earlier work by Mehrdoust, an efficient Monte Carlo simulation algorithm for pricing arithmetic Asian options under Black–Scholes model is proposed. The proposed algorithm has proved extremely successful in decreasing the standard deviation and the error of simulation in pricing of the arithmetic Asian options. In this article, we find that the proposed algorithm under the geometric Brownian motion assumption in the Black–Scholes model can effectively apply for pricing arithmetic Asian options when the stock price process follows the CEV model. Numerical experiments show that our algorithm gives very accurate results.

KEYWORDS:

• Asian option
• CEV model
• Monte Carlo simulation
• Variance reduction

MATHMEAMTICS SUBJECT CLASSIFICATION:

• 35A40
• 35C05
• 65C05
• 60j65

Acknowledgments

The authors thank the Editor and the anonymous referee for their valuable suggestions that improved the presentation of the article.