Estimation the vasicek interest rate model driven by fractional Lévy processes with application

Fractional transport equations for Lévy stable processes.

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the f...

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

Machine Learning Vasicek Model Calibration with Gaussian Processes

In this paper we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The ma...

Application of triangular functions for solving the vasicek model

This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

Conditional Characteristic Functions of Molchan-Golosov Fractional Lévy Processes with Application to Credit Risk

Molchan-Golosov fractional Lévy processes (MG-fLps) are introduced by a multivariate componentwise Molchan-Golosov transformation based on an n-dimensional driving Lévy process. Using results of fractional calculus and infinitely divisible distributions we are able to calculate the conditional characteristic function of integrals driven by MG-fLps. This leads to important prediction results inc...