Swap Market Model: Theory and Empirical Evidence

49 Pages Posted: 20 Oct 2008

See all articles by Bing Gan

Bing Gan

University of Manchester - Manchester Business School

Zhenke Guan

Manchester University - Business School

Ser-Huang Poon

Alliance Manchester Business School, University of Manchester; Alan Turing Institute

Date Written: June 14, 2008

Abstract

This paper tests the co-terminal swap market model (SMM) pricing and hedging performance on Bermudan swaptions. To our knowledge, the drift for SMM is derived explicitly for the first time here, and the procedures for calibration and simulation using a collection of forward swap rates are also shown in detail. The Longstaff-Schwartz least square method is used to approximate the early exercise decision in Bermudan swaption. By introducing individual parameters for volatility of each co-terminal forward swap rate, the model can match the market quoted European swaption price perfectly. It is noted that, for the SMM, one particular volatility formula may not be enough to capture the term structure of different markets. Hedging performance of the model is tested on Euro and USD European co-terminal swaption using a set of swaps as hedge instrument. Principle component analysis (PCA) is adopted to capture the trend of the forward rates' movement and absolute mean of the PCA factors is used for the bumping of forward rate curve. Hedge ratio is calculated based on the delta ratios with respect to PCA factors. P&L of the hedge portfolio generated by co-terminal SMM is examined on Euro and USD market. The result shows that more factors may be needed in order to improve the hedge performance of the model. Nevertheless, the SMM is very similar to LMM in terms of implementation and model performance, and the SMM is more convenient when dealing with exotic interest rate derivatives where swap rate is the underlying.

Keywords: Swap Market Model, Libor Market Model, Bermudan swaptions, Asset-liability management, No-arbitrage Drift

JEL Classification: E43, G13, G21

Suggested Citation

Gan, Bing and Guan, Zhenke and Poon, Ser-Huang, Swap Market Model: Theory and Empirical Evidence (June 14, 2008). Available at SSRN: https://ssrn.com/abstract=1286856 or http://dx.doi.org/10.2139/ssrn.1286856

Bing Gan

University of Manchester - Manchester Business School ( email )

Booth Street West
Manchester, M15 6PB
United Kingdom

Zhenke Guan

Manchester University - Business School ( email )

Aytoun Street
Manchester, M1 3GH
United Kingdom

Ser-Huang Poon (Contact Author)

Alliance Manchester Business School, University of Manchester ( email )

Alliance Manchester Business School
Booth Street West
Manchester, Manchester M15 6PB
United Kingdom
+44 161 275 4031 (Phone)
+44 161 275 4023 (Fax)

HOME PAGE: http://www.manchester.ac.uk/research/Ser-huang.poon/

Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

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