Variational Analysis for the Black and Scholes Equation with Stochastic Volatility

Yves Achdou; Nicoletta Tchou

Displaying similar documents to “Variational Analysis for the Black and Scholes Equation with Stochastic Volatility”

Variational analysis for the Black and Scholes equation with stochastic volatility

Yves Achdou, Nicoletta Tchou (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a...

Doubly reflected BSDEs with call protection and their approximation

Jean-François Chassagneux, Stéphane Crépey (2014)

ESAIM: Probability and Statistics

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We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE....

Approximation of Parabolic Equations Using the Wasserstein Metric

David Kinderlehrer, Noel J. Walkington (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the...