We present a dynamic term structure model in which interest rates of all maturities are bounded from below at zero. Positivity and continuity, combined with no arbitrage, result in only one functional form for the term structure with three sources of risk. One dynamic factor controls the level...

A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree approach. In this note we show that a more direct approach through iterated numerical integration is also possible. A brute force numerical integration would lead to a complexity exponential in...

This paper considers a class of Heath-Jarrow-Morton (1992) term structure models, characterized by time deterministic volatilities for the instantaneous forward rate. The bias that arises from using observed futures yields as a proxy for the unobserved instantaneous forward rate is analyzed. The...

We consider the design and estimation of quadratic term structure models. We start with a list of stylized facts on interest rates and interest rate derivatives, classified into three layers: (1) general statistical properties, (2) forecasting relations, and (3) conditional dynamics. We then...

In continuous time specifications, the prices of interest rate derivative securities depend crucially on the mean reversion parameter of the associated interest rate diffusion equation. This parameter is well known to be subject to estimation bias when standard methods like maximum likelihood...

This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias...

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain...

It is well-known that Gaussian hedging strategies are robust in the sense that they always lead to a cost process of bounded variation and that a superhedge is possible if upper bounds on the volatility of the relevant processes are available, cf. El Karoui, Jeanblanc-Picque and Shreve (1998)...

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps...