标题： 基于一般时间非齐次马尔可夫模型的美式巴黎期权定价 显示英文标题

标题： Pricing American Parisian Options under General Time-Inhomogeneous Markov Models

摘要： 本文提出了通用的方法，基于连续时间马尔可夫链（CTMC）近似，在一般一维时变马尔可夫模型下对各种类型的美式巴黎期权（敲入/敲出、永续/有限期限）进行定价，这些期权具有一般的收益函数。 对于敲入类型，通过条件于巴黎停止时间，我们将定价问题转化为一系列不同期限的普通美式期权的定价问题，并通过将这些期权的价格与巴黎停止时间的分布函数结合，得到美式巴黎敲入期权的价格。 这使得能够通过计算所需数量高效地应用CTMC近似来获得近似期权价格。 在时齐模型下的永续敲入情况中，可以显著减少计算成本。 敲出情况更为复杂，我们使用状态扩展方法来记录波动持续时间，然后通过递归求解一系列变分不等式并使用Lemke的旋转法来获得近似期权价格。 我们证明了在一般时变马尔可夫模型下，所有类型的美式巴黎期权的CTMC近似都收敛，我们的算法的准确性和效率通过大量的数值实验得到了验证。 显示英文摘要

摘要： This paper develops general approaches for pricing various types of American-style Parisian options (down-in/-out, perpetual/finite-maturity) with general payoff functions based on continuous-time Markov chain (CTMC) approximation under general 1D time-inhomogeneous Markov models. For the down-in types, by conditioning on the Parisian stopping time, we reduce the pricing problem to that of a series of vanilla American options with different maturities and their prices integrated with the distribution function of the Parisian stopping time yield the American Parisian down-in option price. This facilitates an efficient application of CTMC approximation to obtain the approximate option price by calculating the required quantities. For the perpetual down-in cases under time-homogeneous models, significant computational cost can be reduced. The down-out cases are more complicated, for which we use the state augmentation approach to record the excursion duration and then the approximate option price is obtained by solving a series of variational inequalities recursively with the Lemke's pivoting method. We show the convergence of CTMC approximation for all the types of American Parisian options under general time-inhomogeneous Markov models, and the accuracy and efficiency of our algorithms are confirmed with extensive numerical experiments.