A robust upwind difference scheme for pricing perpetual American put options under stochastic volatility

Abstract

In this paper, we present an upwind difference scheme for the valuation of perpetual American put options, using Heston's stochastic volatility model. The matrix associated with the discrete operator is an M-matrix, which ensure that the scheme is stable. We apply the maximum principle to the discrete linear complementarity problem in two mesh sets and derive the error estimates. Numerical results support the theoretical results.

Keywords:

• American option
• linear complementarity problem
• stochastic volatility model
• upwind difference scheme
• mixed derivatives

2000 AMS Subject Classifications::

• 65M06
• 65M12
• 65M15

Acknowledgements

We would like to thank the anonymous referees for several suggestions for the improvement of this paper. The work was supported by the Zhejiang Province Natural Science Foundation (Grant Nos. Y6100021, Y6110310) of China and Ningbo Municipal Natural Science Foundation (Grant No. 2010A610099) of China.