Finding of the bonds prices for some stochastic models of interest rate change (Q2784982)

This paper deals with finding of the bonds price of the form \(P(t,r,T)=\exp\{\alpha(t,T)-r(t)\beta(t,T)\}\), where \(\alpha(t,T), \beta(t,T)\) are non-random functions; \(r(t)\) is the interest rate. The author considers the following model of interest rate change \(dr(t)=(a_1(t)+r(t)a_2(t)) dt+\sqrt{b_1(t)+r(t)b_2(t)} dw(t)\), where \(w(t)\) is a Wiener process with \(E[w(t)]=0\), \(Var[w(t)]=\sigma^2t\). In particular, the Merton model, the Cox-Ingersoll-Ross model, the Ho-Lee model, the Black-Derman-Toy model and the Hull-White model are studied.