کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645072 | 1632186 | 2015 | 11 صفحه PDF | دانلود رایگان |
In this paper, we consider a local volatility model with jumps under which the price of a European option can be derived by a partial integro-differential equation (PIDE) with nonconstant coefficients. In order to solve numerically the PIDE, we generalize the implicit method with three time levels which is constructed to avoid iteration at each time step. We show that the implicit method has the stability with respect to the discrete ℓ2ℓ2-norm by using an energy method. We combine the implicit method with an operator splitting method to solve a linear complementarity problem (LCP) with nonconstant coefficients that describes the price of an American option. Finally we conduct some numerical simulations to verify the analysis of the method. The proposed method leads to a tridiagonal linear system at each time step and thus the option prices can be computed in a few seconds on a computer.
Journal: Applied Numerical Mathematics - Volume 87, January 2015, Pages 20–30