Adaptive Willow Tree Models

Willow tree is an efficient option pricing model presented by Curran (1998). Willow tree use constant nodes for each time step to calculate the price and has two main advantage: linear time complexity and linear space complexity. But there is a flaw in Curran’s willow tree: the time’s growth make the price distribute wider, but Curran’s willow tree use constant nodes for each time, that cause the calculation error grow with time’s growth. This thesis present a concept that we can calculate the error at each time for specific number of nodes by using the error function we designed. And adaptively define the number of nodes at each time to control the error. We can trade the increasing of preprocessing time for the decreasing of primary processing time.