Efficient willow tree method for European-style and American-style moving average barrier options pricing
针对移动平均障碍期权定价速度慢的问题，提出两种高效的柳树方法，分别处理离散监测和连续监测情形，在保证精度的同时大幅减少计算时间。
Moving average options are widely traded in financial markets, but exiting methods for pricing this type of option are too slow. This paper proposes two efficient willow tree methods for pricing European-style and American-style moving average barrier options (MABOs). We first solve the finite-dimensional partial differential equation model for discretely monitored MABOs by willow tree methods, and then compute the value of continuously monitored MABOs by Richardson’s two-point extrapolation. Our new willow tree method employs the interpolation error minimization technique to reduce complexity. The corresponding convergence rate and error bounds are also analyzed. It shows that our proposed methods can provide the same accuracy as the binomial tree approach and Monte Carlo simulation, but require much less computing time. The numerical experiments support our claims.