Markov switching regime models have played an increasingly important role in finance and economics, especially for business cycles and long swings in currencies. Regime-switching models provide a simple way to capture stochastic volatility and thus overcomes the drawback of the classical lognormality assumption characterized by constant volatility. This paper considers multivariate Black and Scholes type models with a Markov regime-switching mechanism. We show that the pricing of some multivariate derivatives under models where the Markov chain has two or three states, can be approximated accurately in closed-form, based on linear and quadratic Taylor polynomials. Closed form approximation methods are computationally advantageous as they perform in constant time, compared with alternative methods such as Monte-Carlo, where the accuracy of the estimation is directly linked to the number of executed simulations.

中文翻译：

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转换机制模型下多元衍生品的封闭式近似定价

马尔可夫转换机制模型在金融和经济中发挥着越来越重要的作用，尤其是在商业周期和货币长期波动方面。政权切换模型提供了一种捕获随机波动率的简单方法，从而克服了以恒定波动率为特征的经典对数正态假设的缺点。本文考虑了具有马尔可夫状态切换机制的多元 Black 和 Scholes 类型模型。我们表明，在马尔可夫链具有两个或三个状态的模型下，一些多元导数的定价可以基于线性和二次泰勒多项式以封闭形式准确近似。与蒙特卡罗等替代方法相比，封闭形式逼近方法在计算上具有优势，因为它们在恒定时间内执行，