Interest Rate Model Calibration Using Semidefinite Programming

TITLE: Interest Rate Model Calibration Using Semidefinite Programming.

AUTHORS: Alexandre d'Aspremont

ABSTRACT: We show that, for the purpose of pricing swaptions, the swap rate and the corresponding forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and an approximation formula is derived for such options. This formula is centered around a Black-Scholes price with an appropriate volatility, plus a correction term that can be interpreted as the expected tracking error. The calibration problem can then be solved very efficiently using semidefinite programming.

STATUS: Applied Mathematical Finance 10(3), pp. 183-213, September 2003.

ArXiv PREPRINT: cs.CE/0302034

SOFTWARE: A commercial implementation of the LMM calibration algorithm is available from RaisePartner.

PAPER: Interest Rate Model Calibration Using Semidefinite Programming in pdf