Interest Rate Model Calibration Using Semidefinite Programming
25 Pages Posted: 12 Jul 2004
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.
Keywords: Market model, calibration, semidefinite programming
JEL Classification: C61, G12
Suggested Citation: Suggested Citation
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