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 deriv...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2007-07, Vol.41 (1), p.84-95
Main Authors: Date, P., Mamon, R., Wang, I.C.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Approximation
Cash flow
Cash flow forecasting
Interest rates
Linear equations
Linear models
Linear systems
Stochastic interest rate models
Stochastic models
Stochastic processes
Studies
Uniformly convergent approximation
Valuation
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Summary: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 show applications of the proposed method by pricing default-free and defaultable cash flows. The methodology developed in this paper is applicable to a variety of uncertain cash flow analysis problems.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2006.10.001