Abstract In this paper, we introduce a regime-switching model, such that the volatility of the model depends on the asset price. In this model, the interest rate and the volatility are associated with regime changes. Since the market model has the arbitrage opportunity, we derive an equivalent martingale measure for pricing an arithmetic Asian option. To evaluate the price of an arithmetic Asian option, we propose an efficient variance reduction Monte-Carlo simulation method based on the generation of K -correlated standard normal random vectors. Numerical experiments confirm the success of this method.

中文翻译：

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马尔可夫政权转换模型中亚式期权定价的广义对偶变量蒙特卡罗模拟方法

摘要 在本文中，我们引入了一个政权转换模型，使得模型的波动性取决于资产价格。在这个模型中，利率和波动性与制度变化有关。由于市场模型具有套利机会，我们推导出一个等价的鞅度量来为算术亚洲期权定价。为了评估算术亚洲期权的价格，我们提出了一种基于 K 相关标准正态随机向量生成的有效方差减少蒙特卡罗模拟方法。数值实验证实了该方法的成功。