Discussion Paper Series 2005-E-16

Approximation of Interest Rate Derivatives' Prices by Gram-Charlier Expansion and Bond Moments

Keiichi Tanaka, Takeshi Yamada, Toshiaki Watanabe

In this paper, we develop easily implemented approximations of the prices of several interest rate derivatives. We study swaptions, constant maturity swaps ("CMS"), and CMS options. For swaption prices, we approximate swaption prices under one forward measure by using a Gram-Charlier expansion. This expansion is an orthogonal decomposition of a density function in additive form and involves bond moments in the coefficients. Hence, the swaptions price can be approximated easily and accurately. Higher-order approximations yield very accurate prices enough to price each transaction, and lower-order approximations are suitable for portfolio evaluation and risk management. In addition, we approximate CMS rates by using bond moments. We also approximate prices of CMS options by combining the two methods.

Keywords: Gram-Charlier expansion, bond moment, swaption, constant maturity swap, convexity adjustment

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2005 Bank of Japan All Rights Reserved.

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