Cholesky Decomposition for the Vasicek Interest Rate Model

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim’s equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optim...

On Non-existence of a One Factor Interest Rate Model for Volatility Averaged Generalized Fong–vasicek Term Structures

We study the generalized Fong–Vasicek two-factor interest rate model with stochastic volatility. In this model dispersion is assumed to follow a non-negative process with volatility proportional to the square root of dispersion, while the drift is assumed to be a general function. We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged b...

Low Rank Updates for the Cholesky Decomposition

Usage of the Sherman-Morrison-Woodbury formula to update linear systems after low rank modifications of the system matrix is widespread in machine learning. However, it is well known that this formula can lead to serious instabilities in the presence of roundoff error. If the system matrix is symmetric positive definite, it is almost always possible to use a representation based on the Cholesky...

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...