Interpolation of Discount Factors

This paper deals with the problem of interpolation of discount factors betweentime buckets. The problem occurs when price and interest rate data of a marketsegment are assigned to discrete time buckets. A simple criterion is developed inorder to identify arbitrage-free robust interpolation methods. Methods closelyexamined include linear, exponential and weighted exponential interpolation.Weighted exponential interpolation, a method still preferred by some banks andalso offered by commercial software vendors, creates several problems andtherefore makes simple exponential interpolation a more logical choice. Linearinterpolation provides a good approximation of exponential interpolation for asufficiently dense time grid.