Stochastic Mesh Methods for Hörmander Type Diffusion Processes
- First Online:
In the present paper the authors discuss the efficiency of stochastic mesh methods introduced by Broadie and Glasserman (J Comput Finance 7(4):35–72, 2004). The authors apply stochastic mesh methods to certain type of Hörmander type diffusion processes and show the following. (1) If one carefully takes partitions, the estimated price of American option converges to the real price with probability one. (2) One can obtain better estimates by re-simulation methods discussed in Belomestny (Finance Stoch 15:655–683, 2011), although the order is not so sharp as his result.
Key wordsComputational finance Malliavin calculus Option pricing Stochastic mesh method
- 1.Avramidis, A.N., Hyden, P.: Efficiency improvements for pricing American options with a stochastic mesh. In: Proceedings of the 1999 Winter Simulation Conference, pp. 344–350 (1999)Google Scholar
- 2.Avramidis, A.N., Matzinger, H.: Convergence of the stochastic mesh estimator for pricing American options. J. Comput. Finance 7(4), 73–91 (2004)Google Scholar
- 8.Shigekawa, I.: Stochastic Analysis. Translation of Mathematical Monographs, vol. 224. AMS, Providence (2000)Google Scholar