Abstract
In this paper, we explore two new tree lattice methods, the piecewise binomial tree and the piecewise trinomial tree for both the bond prices and European/American bond option prices assuming that the short rate is given by a generalized skew Vasicek model with discontinuous drift coefficient. These methods build nonuniform jump size piecewise binomial/trinomial tree based on a tractable piecewise process, which is derived from the original process according to a transform. Numerical experiments of bonds and European/American bond options show that our approaches are efficient as well as reveal several price features of our model.
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