Alessandro Ramponi

A REVIEW OF TECHNIQUES FOR THE ESTIMATION OF THE TERM STRUCTURE

A number of techniques have been proposed for estimating the term structure, yet solid theoretical foundations and a comparative assessment of the results produced by these techniques are not available. In the present paper we prove, within a well defined mathematical setting, how the existence of discount factors is possible only if the condition of absence of static arbitrage is fulfilled. Besides that we report the results of an extensive set of tests whose scope is to show how the most widely used approaches in this field behave on both real and synthetic data.

ADAPTIVE AND MONOTONE SPLINE ESTIMATION OF THE CROSS-SECTIONAL TERM STRUCTURE

A number of numerical methods based on a piecewise polynomial approximation have been proposed for the estimation of the term structure of interest rates. Some drawbacks have been pointed out, such as a possible non monotonic estimated discount function and a highly fluctuating spot and forward rates. In order to overcome these kind of problems, we study the feasibility of an adaptive regression spline technique which use a monotone basis together with two alternative knot location procedures: a deterministicgreedyalgorithm and its randomized version in a simulated annealing framework. The features of the proposed method are tested on a set of data.

Option pricing in a hidden Markov model of the short rate with application to risky debt evaluation

Following the path initiated by Merton (1973), we study the option pricing problem in an economy with stochastic interest rates. We model the short rate dynamic by a diffusion process whose parameters are modulated by an underlying Markov process with jumps, as in Landen (2000). By exploiting the change of numeraire technique we obtain, under some assumption, a simple and easy to use call pricing formula which we then apply to the evaluation of risky debts so enlarging the flexibility of previous results obtained by Shimko et al. (1993). We also provide a detailed numerical study of call prices and credit spreads for a straightforward but interesting extension of the Vasicek dynamic included in our model.

On a Transform Method for the Efficient Computation of Conditional V@R (and V@R) with Application to Loss Models with Jumps and Stochastic Volatility

In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an elementary optimization problem of convex type in one dimension. An application to univariate loss models driven by Lévy or stochastic volatility risk factors dynamic is finally reported.