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Date
2004-09Type
- Report
ETH Bibliography
yes
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Abstract
Prices of European plain vanilla as well as barrier and compound options on one risky asset in a Black-Scholes market with stochastic volatility are expressed as solution of degenerate parabolic partial differential equations with two spatial variables: the spot price $S$ and the volatility process variable $y$. We present and analyze a pricing algorithm based on sparse wavelet space discretizations of order $p\geq 1$ in the spot price $S$ or the log-returns $x=\log S$ and in $y$, the volatility driving process, and on $hp$-discontinuous Galerkin time-stepping with geometric step size reduction towards maturity $T$. Wavelet preconditioners adapted to the volatility modelsfor a GMRES solver allow to price contracts at all maturities $0 Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Stochastic volatility models; Degenerate parabolic partial differential equations; Weighted Sobolev spaces; Discontinuous Galerkin time stepping; Compound Options; Sparse Tensor products; Hyperbolic cross approximationsOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Related publications and datasets
Is previous version of: http://hdl.handle.net/20.500.11850/38322
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ETH Bibliography
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