用Homotopy方法解随机波动率远期LIBOR模型中利率衍生品定价问题

Homotopy analysis for derivatives pricing in a LIBOR market model with stochastic volatility

为深入研究固定收益衍生品的定价问题,在波动率为相应的远期测度下的Ornstein-Uhlenbeck过程的模型框架下,给出了利率上限和债券期权的定价公式.同时,应用Homotopy方法解决了定价公式中产生的偏微分方程,使其以函数级数和的形式表示出来.并对级数和形式的解的收敛性进行了相应的分析.

In order to address the pricing problems of fixed income derivatives in the context of stochastic volatility, the Homotopy analysis method was applied to give the pricing formula of caplet and bond option in a LIBOR market model with stochastic volatility in which the volatility is an Ornstein-Uhlenbeck process under corresponding forward measure, in which Homotopy method was applied to solve a PDE. With such method, the solution, i.e. the pricing formula comes in as a sum of summands derived from previous summand. And a convergence analysis is given.