Modelling Australian interest rate swap spreads by mixture autoregressive conditional heteroscedastic processes

An interest rate swap is a contract between two parties to exchange periodically fixed rate payments for floating rate payments based on an agreed-upon notional principal and maturity. The fixed rate is known as the swap rate and a swap curve can be constructed using swap rates of different maturities. The swap curve is widely used by financial market participants as the benchmark for the pricing of investment grade corporate bonds. The floating rate is usually the Bank Bill Swap Reference Rate (BBSW) in the Australian market. The Australian interest rate swap market is the most important over-the-counter (OTC) derivative market in Australia. The outstanding notional amount at the end of June 2006 was US$815.8 billion, which was much greater than other derivative instruments such as the forward rate agreements and interest rate options. The swap market size is comparable to the stock market in Australia, which had a market capitalisation of US$893.3 billion at the end of June 2006. The observed difference between the swap rate and the government bond yield of corresponding maturity is known as the swap spread. The swap spread reflects the risk premium that is involved in a swap transaction instead of holding risk-free government bonds. It is primarily composed of the liquidity risk premium and the credit risk premium. In recent years there has been growing interest in modelling swap spreads because the swap spread is the key pricing variable for the swap rate. In this paper we apply the class of mixture autoregressive conditional heteroscedastic (MARCH) models to three (3-year, 5-year and 10-year) swap spread series in Australia. The MARCH model is able to capture both of the stylised characteristics of the observed changes of the swap spread series: volatility persistence and the dependence of volatility on the level of the data. The proposed MARCH model also allows for regime switches in the swap spreads. A MARCH (2; 3,0; 1,0) model is consistently identified for the three observed series. The fitted MARCH models can be interpreted as AR(3)– ARCH(1) processes mixed with small portions (5% to 10%) of independent shocks/breaks. In addition, we use the ex ante conditional probabilities as a tool for detecting possible shocks in the swap spread data. Around 50 observations of the 5-year swap spread series are identified as likely to come from the shock component. These detected shocks are mainly from the fourth quarter of 2001 (after terrorist attacks in the United States on 11 September 2001) and the summer of 2003 (retreat of mortgagebacked securities convexity hedging in the United States).