A Vasicek-Type Short Rate Model With Memory Effect

A Comparative Study of the Vasicek and the CIR Model of the Short Rate

In this work, we analyze two important and simple models of short rates, namely Vasicek and CIR models. The models are described and then the sensitivity of the models with respect to changes in the parameters are studied. Finally, we give the results for the estimation of the model parameters by using two different ways.

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...

Optimal Consumption Problem in the Vasicek Model

We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumpti...

Calculating credit risk capital charges with the Vasicek model

Even in the simple Vasicek credit portfolio model, the exact contributions to credit value-at-risk cannot be calculated without Monte-Carlo simulation. As this may require a lot of computational time, there is a need for approximative analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy and T. Wil...