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Pricing Financial Instruments: The Finite Difference Method
Curt Randall,Domingo Tavella +1 more
TLDR
The Pricing Equations. as mentioned in this paper and the Finite-difference method are the most commonly used methods for finite difference methods in the literature, and they can be found in:Abstract:
The Pricing Equations. Analysis of Finite Difference Methods. Special Issues. Coordinate Transformations. Numerical Examples. Index.read more
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Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach
TL;DR: In this article, the stability of the numerical solution of a multi-asset American option pricing problem is analyzed for the first time and sufficient stability conditions on step sizes, that also guarantee positivity and boundedness of the solution, are found.
DissertationDOI
Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing
TL;DR: In this paper, numerical analysis and computing of finite difference schemes for several relevant option pricing models that generalize the Black-Scholes model are provided. And a careful analysis of desirable properties for the numerical solutions of option pricing model such as positivity, stability and consistency are provided, in order to handle the free boundary that arises in American option pricing problems.
Journal ArticleDOI
Variable time-stepping hybrid finite difference methods for pricing binary options
Hongjoong Kim,Kyoung Sook Moon +1 more
TL;DR: Numerical experiments for standard European vanilla, bi-nary, and American options show that both Type I and II variable timestep methods are much more e ARTICLEcient than the fully implicit method orhybrid methods with uniform time steps.
DissertationDOI
On accurate and efficient valuation of financial contracts under models with jumps
TL;DR: A new numerical method is derived for the classical problem of pricing vanilla options quickly in time-changed Brownian motion models based on rational function approximations of the Black-Scholes formula, which is able to work out implied volatilities more efficiently than is possible using other common methods.
Journal ArticleDOI
An adjoint method for the exact calibration of stochastic local volatility models
Maarten Wyns,Karel in 't Hout +1 more
TL;DR: In this paper, an adjoint semidiscretization of the corresponding forward Kolmogorov equation is used to obtain an expression for the leverage function in the pertinent SLV model such that the approximated fair values defined by the SLV and SLV models are identical for non-path-dependent European-style options.