The Fokker-Planck equation: methods of solution and applications by H. Risken

The Fokker-Planck equation: methods of solution and applications H. Risken ebook
Format: djvu
Publisher: Springer-Verlag
ISBN: 0387130985, 9780387130989
Page: 485

2 gives the calculated probability distribution for the BS and OU models, using the second derivative numerical method, compared to their exact analytic solutions. The SLV Calibrator then applies to this PDE solution a Levenberg-Marquardt optimizer and finds the (time bucketed) SV parameters that yield a maximally flat leveraged local volatility surface. Then, using a non-linear Fokker-Planck equation, one adds a SV component and for any given set of SV parameters computes a new "leveraged local volatility surface" that still matches the vanillas, while accommodating SV. €tree” algorithms are often used, corresponding to the above Langevin and Fokker-Planck equations [14,15]. A formal analogy of the Fokker–Planck equation with the Schrodinger equation allows the use of advanced operator techniques known from quantum mechanics for its solution in a number of cases. Risken: The Fokker–Planck Equation: Methods of Solution and Applications (Springer-Verlag, Berlin, 1996). These algorithms have typically been .. Other techniques, such as path integration have also been used, What is important in this application is that the Fokker–Planck equation can be used for computing the probability densities of stochastic differential equations. Tree algorithms are generally derived from binomial random walks [13]. The main method of solution is by use of the Fokker-Planck equation (b), which provides a deterministic equation satisfied by the time dependent probability density. Risken: The Fokker-Planck Equation: Methods of Solution and Applications (Springer, Berlin, 1989) 2nd ed.