Infinite Horizon Forward Backward Stochastic Differential Equations And Numerical Method For Pricing Consol Bonds

In this paper, we consider to price some interest rate products like consol bonds. The similar products are such as the A shares of securities investment classification funds and preferred stocks which are about to be published. Nevertheless, the payments of interest of these products are not unchangeable. So we have made some further research of the work of Duffie, Ma and Yong. In this way, we can deal with the valuation problem of adjustable rate consol bonds.In order to solve the valuation problem of consol bonds, we try to contain more cases from theoretical aspects. The forward backward stochastic differential equation(FBSDE) which we will deal with can both deal with adjustable rate bonds and describe the ambiguity of the investors. Hence, we have proved the existence and uniqueness of the infinite horizon FBSDE below, which is more widely to be used.This expanded equation can help us to deal with the valuation problem of adjustable rate consol bonds. We explored and proved some connections of condi-tional expectation of discounted form of bonds and the adapted solution of forward backward stochastic differential equation. By this mean, we could get the fair val-ue of consol bonds through solving a corresponding forward backward stochastic differential equation.After that, we consider to give a numerical algorithm which is designed to solve the infinite horizon problem. The idea is simple, we use the finite horizon problem to approximate the infinite horizon problem. And we use the enhanced four step scheme to solve the finite horizon problem numerically, which we substitute Milstein method to Euler method. Through the discuss of approximability of the solution, we have got the estimation of the convergence order, which the solution converges exponentially with respect to the time horizon T and converges linearly with respect to grid spacing.At last, we presented a numerical example and gave some advices of parameter settings. For stringency, we also considered the numerical example of degenerate case and a complex example of other writers.