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...

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash-flows, when the discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho-Lee model. Upper and lower bounds in convexity order are obtained. The high accuracy of the method is illustrated for cash-flows for which no...

Even in the simple Vasicek one-factor 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 approximate analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy a...

We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipović, and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate rt. We give condit...

The aim of this paper is twofold; first we concentrate on the work of Vasicek (1977) and Cox, Ingersoll and Ross (1985). We examine and test empirically each model and discuss its performance in predicting the term structure of interest rates using a parametric estimating approach GMM (Generalized Moments Method). Second we estimate the term structure of interest rate dynamics using a nonparame...

In old accounting tradition, non-life insurance companies have estimated nominal claims reserves for their outstanding loss liabilities. The new Solvency II developments require from non-life insurance companies that they go over to a market-consistent valuation of their insurance liabilities (full balance sheet approach) and that they prove solvency on a yearly basis. As a consequence non-life...

This paper develops a simple model for pricing interest rate options. Analytical solutiorls are developed for European claims and extremely efficient algorithms exist for tile pricing of American opciolls. T h e interest rate claims are priced in the Heath-Jarrow-klorto~i paradigm, and hence illcorporate full information on the term structure. T h e volatility. structure for forward rates is hu...