Iterative Methods for Pricing American Options under the Bates Model | Zendy

Santtu Salmi | Zendy; Jari Toivanen | Zendy; Lina von Sydow | Zendy

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Iterative Methods for Pricing American Options under the Bates Model

Author(s) -

Santtu Salmi,

Jari Toivanen,

Lina von Sydow

Publication year - 2013

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2013.05.279

Subject(s) - discretization , computer science , bates , mathematics , mathematical optimization , scalability , valuation of options , stochastic volatility , gaussian quadrature , multigrid method , iterative method , volatility (finance) , integral equation , algorithm , partial differential equation , econometrics , mathematical analysis , nyström method , database , engineering , aerospace engineering

We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG method leads to better scalability than the projected SOR (PSOR) method when the discretization is refined

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