Common Correlation and Calibrating the Lognormal Forward Rate Model

The Lognormal forward rate version of the Libor model is very useful for pricing and hedging exotic OTC products such as auto-caps and in-arrear swaps. However, the model is not easy to calibrate because its parameters include forward rate correlations that are difficult to forecast, particularly at the short end. To gain some idea of how these correlations change, Figure 1 shows the average daily correlations between semi-annual forward rates in the UK during four three month periods between June 2001 and June 2002. It is clear that changes in correlation are not as significant at the long end as they are at the short end. Figure 2 shows the correlation between the semi-annual forward rate starting in six months, and several longer maturity semi-annual forward rates starting in one year, 18 months, 2 years and so forth. Each line in Figure 2 represents the average daily correlation during a quarterly period. The correlations between the six month forward rate and