The Forward Rates for Multifactor Model of Term Structure “With Square Root”

Abstract

The multi-factor model “with square root” is discussed in details. For such model, the representation of state variable process in the integral form is derived and its covariance matrix is found. The special attention to the problem connected with the tendency for the term structure of long-term forward rates to slope downwards is given. For multi-factor models with square root the following results are derived: representations of the forward rate curve through the volatility of the state variable process and through the volatility of zero coupon yield process are obtained; the expectations, variances and co-variances for the forward rates and the yield process volatility are calculated; the expectation and the variance for the derivative of forward rate are found; the Brown − Schaefer approximation for the spread of forward rate is examined. As examples two three-factor models (BDFS and Chen models) are examined. On the basis of the estimates of parameters of these models received by empirical way the numerical analysis including calculation of covariance matrices of process of state variables, calculation of an expectation of the local variance of yield process and calculation of the variance of zero coupon yield have been fulfilled.