Recursive Marginal Quantization of Higher Order Schemes

Tue, 06/09/2016 - 5:30pm

Thomas A. McWalter, University of Cape Town and University of Johannesburg


Commonwealth Bank, Level 19, Darling Park Tower 1, 201 Sussex Street, Sydney NSW 2000


Recursive Marginal Quantization of the Euler scheme has recently been proposed by Sagna and Pag├Ęs (2015) as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations. This method involves an algorithm that recursively quantizes the conditional marginals of the discrete-time Euler approximation process. The main innovation in their work was to show that this approach converges. By generalizing their approach, we show that it is possible to perform recursive marginal quantization for two higher order schemes: the Milstein scheme and the simplified order 2.0 scheme. To illustrate the gains in performance, we provide some numerical comparisons. Initially, we directly compare the marginal densities generated by the various quantizers with the known transition density at each successive time step for the log-normal, square-root and CEV processes. This graphically demonstrates the improved performance of the Milstein and simplified order 2.0 schemes. The schemes are then used to price continuously and discretely monitored barrier options under a quadratic-normal volatility model, thereby allowing further performance comparisons.

Sponsored by Commonwealth Bank

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