In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional Itô-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently regular density. In this article we first prove results on absolute continuity for laws of projected jump-dif...

Formulae for the distribution of the losses of a loan portfolio that are both realistic and simple enough to be implemented in a spreadsheet are hard to come by. The most prominent example is the Vasicek (1987) formula which is based upon a simplified version of the multivariate Merton (1974) model. Using an algorithm from the theory of Archimedean Copula functions, this paper gives some more l...

This project describes credit default swap (CDS) and shows how to calculate a fair value for such a contract. The stochastic evaluation of both the interest rate and the default intensity are first studied independent by using one factor a Vasicek model for a bond and a one factor model for the probability of no default. After validations the combined effect of stochastic interest rates and def...

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...

This paper studied an optimal reinsurance and investment problem for insurers under the mean-variance criterion in the stochastic interest rate and stochastic volatility environment, where the financial market consists of two assets: one is the risk-free asset (i.e bond) and the other is the risky-asset (i.e stock) whose volatility satisfying the Heston model. Assume that the interest rate is d...

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates, domestic gross products or supply and demand rates, we propose a fractional Brownian motion (fBm) driven model to describe the dynamics of the short rate in a bond market as well as the default rate for possible default. We aim at results analogous to those achieved in recent years for affin...

T he term structure models discussed in our previous article (“Term Structure of Interest Rates,” MiER Vol. 7, No. 3) such as the [Vasicek 1978] or the [CoxIngersoll-Ross 1985] model may not match the current term structure. The Black-Derman-Toy (BDT) and BlackKarasinksi models discussed in this article are important examples of models in which the current term structure can always be replicated.

We compare the durations of corporate and Treasury bonds in the reducedform, intensity based credit risk modeling framework. In the case where default risk is independent of default-free interest rates, we provide in each of the three most popular recovery regimes a sufficient condition under which the duration of the corporate bond is smaller than the duration of a similar Treasury bond. In th...

Endowment insurance with a participating policy is an contract that offers death benefits increase every year. This paper analyzes single and monthly premiums of endowment life using the Vasicek interest rate model. The in highly dependent on performance company's investment portfolio. model this study assumes market rates move stochastically following portfolio follows geometric brownian motio...