Nonaffine Models of Yield Term Structure

Abstract

The equation of term structure for the price of a zero-coupon bond is considered, the solution of which in analytical form is known, basically, for the simplest models and has an affine structure with respect to the short-term rate. The paper constructs solutions of this equation for a family of term structure models that are based on short-term rate processes in which the square of volatility is proportional to the third power of the short-term rate in stochastic differential equations. The solution of the equation is sought in the form of a definite functional series and, as a result, is reduced to a confluent hypergeometric function. Three versions of the underlying stochastic differential equations for short-term rate processes are considered: with zero drift, linear drift, and quadratic drift. Numerical examples are given for the yield curve and the forward rate curve for these versions. Some conditions for the existence of nontrivial solutions of the equation of time structure in the family of processes under consideration are formulated.