A New Howard–Crandall–Douglas Algorithm for the American Option Problem in Computational Finance
- 326 Downloads
The unavailability of a closed-form formula for the American option price means that the price needs to be approximated by numerical techniques. The valuation problem can be formulated either as a linear complementarity problem or a free-boundary value problem. Both approaches require a discretisation of the associated partial differential equation, and it is common to employ standard second-order finite difference approximations. This work develops a new procedure for the linear complementarity formulation. Howard’s algorithm is used to solve the discrete problem obtained through a higher-order Crandall–Douglas discretisation. Speed and error comparisons indicate that this approach is more efficient than the procedures for solving the free-boundary value problem.
KeywordsComputational finance American option Policy iteration Howard’s algorithm
- 4.Elliott, C.M., Ockendon, J.R.: Weak and variational methods for moving boundary problems. Research notes in Mathematics, Pitman, Boston, Mass. 59 (1982)Google Scholar
- 5.Howard, R.A.: Dynamic Programming and Markov Processes. The MIT Press, Cambridge, MA (1960)Google Scholar
- 8.Seydel, U.R.: Tools for Computational Finance. Springer-Verlag, Heidelberg (2006)Google Scholar
- 10.Saib, A.A.E.F., Tangman, D.Y., Thakoor, N., Bhuruth, M.: On some finite difference algorithms for pricing American options and their implementation in Mathematica. In: Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering, pp. 1029–1040. Alicante, Spain (2011)Google Scholar