American option pricing problem transformed on finite interval

作者：Gyulov T B^*; Valkov R L

来源：International Journal of Computer Mathematics, 2016, 93(5): 821-836.

DOI：10.1080/00207160.2014.906587

• linear complementarity problem
• degenerate parabolic operator
• monotonic penalty method
• fitted finite volume method
• 65K15
• 65M08
• 49J40

We study the American option pricing linear complementarity problem (LCP), transformed on finite interval as it is initially defined on semi-infinite real axis. We aim to validate this transformation, investigating the well-posedness of the resulting problem in weighted Sobolev spaces. The monotonic penalty method reformulates the LCP as a semi-linear partial differential equation (PDE) and our analysis of the penalized problem results in uniform convergence estimates. The resulting PDE is further discretized by a fitted finite volume method since the transformed partial differential operator degenerates on the boundary. We show solvability of the semi-discrete and fully discrete problems. The Brennan-Schwarz algorithm is also presented for comparison of the numerical experiments, given in support to our theoretical considerations.

• 出版日期2016-5-3