Paper Info
Title
Lagrange Multiplier Approach with Optimized Finite Difference Stencils for Pricing American Options under Stochastic Volatility
Abstract
The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear complementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values, while for large asset values and variance a standard truncation is used. The finite difference discretization is constructed by numerically solving a quadratic optimization problem aiming to minimize the truncation error at each grid point. A Lagrange approach is used to treat the linear complementarity problems. Numerical examples demonstrate the accuracy and effectiveness of the proposed approach.
Year
DOI
Venue
2009
10.1137/07070574X
SIAM J. Scientific Computing
Keywords
Field
DocType
truncation error,multigrid method,optimized finite difference stencils,quadratic programming,lagrange approach,american option pricing,standard truncation,lagrange multiplier approach,deterministic numerical valuation,flnite difierence method,stochastic volatility,lagrange method,penalty method,linear complementarity prob- lem,quadratic optimization problem,stochastic volatility model,pricing american options,linear complementarity problem,numerical example,large asset value,new truncation,spatial variability,quadratic program,second order,finite difference,finite difference method,lagrange multiplier,quadratic optimization,stochastic process,empirical evidence
Truncation,Stochastic volatility,Truncation error,Mathematical optimization,Complementarity theory,Finite difference method,Stochastic modelling,Truncation error (numerical integration),Linear complementarity problem,Mathematics
Journal
Volume
Issue
ISSN
31
4
1064-8275
Citations 
PageRank 
References 
15
1.68
9
Authors
2
Name
Order
Citations
PageRank
Kazufumi Ito1833103.58
Jari Toivanen239743.84