Examining the Leptokurtic Property in Stephen Kou Pricing Modeling Based on Variance Reduction Method - Monte Carlo Simulation

Subject Areas : Financial Economics

Kianoush Fathi vajargah ^{1 *} , Hossein Eslami Mofid Abadi ²

1 - Department of Statistics Islamic Azad University, North branch Tehran, Iran
2 -

Received: 2025-04-29 Accepted : 2025-06-09 Published : 2025-07-02

Keywords: Kou Model, Barrier Option, Monte Carlo Simulation, Leptokurtic Property.,

Abstract :

The asymmetric characteristics of the leptokurtic distribution are skewed to one side and have a tall peak and heavy tails compared to the normal distribution, as empirically observed. The Black-Scholes model utilizes Brownian motion for option pricing; however, data from financial markets exhibit jumps in prices, stochastic volatility, and skewness compared to the normal distribution. To improve the performance of Black-Scholes, jumps need to be incorporated into asset pricing models. One of the research issues in the financial world is the pricing and hedging of options. In this research, the model of jump sizes with a double-exponential distribution by Stephen Kou is employed. Additionally, the Stephen Kou model is capable of generating the leptokurtic characteristics of the return distribution and sudden jump observations in option prices. Monte Carlo simulation is also a widely used tool for option pricing. However, its effectiveness is heavily dependent on the use of successful variance reduction techniques. In this paper, barrier options are utilized. Furthermore, a control variate method is employed for variance reduction. Therefore, this research investigates the role of changing the amounts of barrier options based on the leptokurtic characteristics in the model. Consequently, the results indicate that increasing the level of barrier options leads to an increase in options prices. Additionally, the results show that raising the level of barrier options has a significant impact on reducing variance.

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