论文标题
采用有效的混合方法，用于具有随机波动性资产的定价障碍选项
Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility
论文作者
论文摘要
我们结合了一维蒙特卡洛模拟和半分析的一维热潜在方法，以设计有效的技术，用于具有相关随机波动率的资产上的定价障碍选项。我们的障碍选项估值方法利用了两个循环。首先，我们通过通过蒙特卡洛方法生成波动率路径来运行外循环。其次，我们在给定的波动率路径上调节价格动态，并应用热电位的方法来解决内部环中封闭形式的条件问题。我们通过将半分析方法与二维Monte Carlo模拟和混合方法进行比较来说明我们的半分析方法的准确性和疗效，该方法结合了内部环的有限差分技术和外部环的蒙特卡洛模拟。我们将我们的方法应用于状态概率（绿色功能），生存概率和呼叫选项值的值。我们的方法提供了更好的准确性，并且比现有方法更快。 s是我们分析的副产品，我们将Willard（1997）的条件公式推广到路径独立选项的估值中，以依赖路径依赖性选项，并为漂移的Brownian运动及其运行最小值的价值的关节概率密度提供了新颖的表达。
We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach to barrier options valuation utilizes two loops. First we run the outer loop by generating volatility paths via the Monte Carlo method. Second, we condition the price dynamics on a given volatility path and apply the method of heat potentials to solve the conditional problem in closed-form in the inner loop. We illustrate the accuracy and efficacy of our semi-analytical approach by comparing it with the two-dimensional Monte Carlo simulation and a hybrid method, which combines the finite-difference technique for the inner loop and the Monte Carlo simulation for the outer loop. We apply our method for computation of state probabilities (Green function), survival probabilities, and values of call options with barriers. Our approach provides better accuracy and is orders of magnitude faster than the existing methods. s a by-product of our analysis, we generalize Willard's (1997) conditioning formula for valuation of path-independent options to path-dependent options and derive a novel expression for the joint probability density for the value of drifted Brownian motion and its running minimum.
