标题： SABR和Heston方程的半解析路径积分解：定价欧式和亚式期权 显示英文标题

标题： Semi-analytic path integral solution of SABR and Heston equations: pricing Vanilla and Asian options

摘要： 我们讨论一种基于路径积分的半解析方法，用于求解SABR型方程。 在此方法中，一组变量通过解析方式积分，而第二组变量则通过蒙特卡洛方法进行数值积分。 这种方法在文献中被称为条件蒙特卡洛，能够得到关于三个相关随机变量的紧凑表达式。 当在具有时间依赖参数的SABR、Heston和Bates模型中求解欧式期权定价时，该方法具有实用性和高效性。 此外，它还可以实际应用于$\beta=0$SABR模型中的亚式期权定价以及其他$\beta=0$类型模型。 显示英文摘要

摘要： We discuss a semi-analytical method for solving SABR-type equations based on path integrals. In this approach, one set of variables is integrated analytically while the second set is integrated numerically via Monte-Carlo. This method, known in the literature as Conditional Monte-Carlo, leads to compact expressions functional on three correlated stochastic variables. The methodology is practical and efficient when solving Vanilla pricing in the SABR, Heston and Bates models with time depending parameters. Further, it can also be practically applied to pricing Asian options in the $\beta=0$ SABR model and to other $\beta=0$ type models.