A survey of stochastic continuous time models of the term structure of interest rates (Q1333590)

The paper reviews financial economic literature on stochastic continuous time models of the term structure of interest rates, i.e. on models for the valuation of pure discount bonds. The attention is focused exclusively on the models where the state variable follows diffusion processes. Section 2 presents a standard continuous time arbitrage pricing model and then it concentrates on the case of a pure discount bond relating its price to the expectation of the exponential path of the instantaneous risk free interest rate under the equivalent martingale measure. Sections 3 and 4 describe the single factor and multiple factor models, respectively. Section 5 (Arbitrage vs. equilibrium models) deals with the specification of the market prices of risk of the factors. Section 6 examines the models which are designed to perfectly replicate the current term structure (they can be used e.g. for improved valuation of derivative securities). Section 7 reviews the existing empirical evidence in this context.