Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Sonia Petrone
Universita' Bocconi, Milano, Italy
"Dynamic polynomial regression models for the term structure of interest rates"
ABSTRACT
The problem of estimating the discount function, which is of interest in finance, can be regarded as a regression problem where the regression function has a dynamic evolution, subject to some constraints (the no-arbitrage restrictions). The aim is to obtain a dynamic model which gives a good fit of the market prices but at the same time allows to control for no-arbitrage or quasi no-arbitrage conditions. We first discuss a polynomial regression model where an arbitrage-free dynamics is introduced on the curve through the polynomial coefficients. However, we argue that, due to market frictions, the price process might be only approximately arbitrage-free. Furthermore, a polynomial model might suffer of a specification error; in this case, the polynomial model should be regarded as an approximation of the theoretical, arbitrage-free curve. Consequently, we take a different approach. Rather than imposing exact no-arbitrage to the polynomial model, we study how the arbitrage-free evolution of the theoretical curve reflects on its polynomial approximation. We are able to give a simple answer to this question by using constructive polynomials, namely Bernstein polynomials. We show two properties of quasi-no-arbitrage for the proposed model. The model can be written in a state-space form, and estimation can be obtained by filtering procedures. The performance of our model is illustrated in an example with real data.
Thursday, February, 12, 2004
4:00 - 5:00 pm
208 Patterson Hall
Refreshments will be served on the second floor of Patterson Hall (outside Room 208) at 3:45 pm.