Interest Rate Model Calibration Using Semidefinite Programming

Details Interest Rate Model Calibration Using Semidefinite Programming Interest Rate Model Calibration Using Semidefinite Programming

2003-02-25

arxiv.org/abs/cs/0302034v2

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

Computer Science

Computational Engineering, Finance, and Science

Scientific paper

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.

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