Valuation of Cash Flows under Random Rates of Interest: A Linear Algebraic Approach

This paper reformulates the classical problem of cash flow valuation under stochastic discount factors into a system of linear equations with random perturbations. Using convergence results, a sequence of uniform approximations is developed. The new formulation leads to a general framework for deriving approximate statistics of cash flows for a broad class of models of stochastic interest rate process. We then show applications of the proposed method by pricing default-free and defaultable bonds. The methodology developed in this paper is applicable for a variety of uncertain cash flow analysis problems. Key words: Statistical methods, stochastic interest rate model