Generation of scenarios for the interest rates under the arbitrage-free dynamic Nelson-Siegel model

Abstract

The affine Arbitrage-Free Dynamic Nelson-Siegel model (AFDNS) introduced by Christensen, Diebold and Rudebusch in 2007 provides an interesting alternative model for pricing and risk management, since it maintains the theoretical arbitrage-free restrictions of affine models and provides remarkably empirical properties. Our purpose in this paper is to provide the analysis and formulas required in the generation of scenarios for the interest rates at future time-horizons, under this model. Such simulations are required in various contexts, as in the pricing of interest rates derivatives and in the valuation of insurance firms' risk capital.