Swap Market Model: Theory and Empirical Evidence

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.