PDE-regularization for pricing multi-dimensional Bermudan options with Monte Carlo simulation
(English)Manuscript (preprint) (Other academic)
This paper considers the problem of pricing multi-dimensional Bermudan derivatives using Monte Carlo simulation. A new method for computing conditional expectations is proposed, which combined with the dynamic programming principle provides a way of pricing the derivatives.
The method is a non-parametric projection with regularization. The regularization penalizes deviations from the PDE that the true conditional expectation satisfies. The point being that it is less costly to compute the norm of the PDE than it is to solve it, thus avoiding the curse of dimensionality.
The method is shown to produce accurate numerical results in multi-dimensional settings, given a good choice of the regularization parameter. It is illustrated with the multi-dimensional Black-Scholes model and compared to the Longstaff-Schwartz approach.
Optimal stopping, regularization, non-parametric estimation, conditional expectations, Bermudan options, Snell envelope.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-120477OAI: oai:DiVA.org:kth-120477DiVA: diva2:615247
QS 20132013-04-092013-04-092013-04-16Bibliographically approved