Interest Rate Models

Jiří Witzany

Chapter 7 in Derivatives, 2020, pp 261-287 from Springer

Abstract: Abstract The Standard Market Model developed and applied in the previous chapter assumes that interest rates or bond prices are lognormally distributed. The model does not describe the stochastic dynamics of interest rates over time, and so it cannot be applied to value American-style options, callable bonds, or other more complex interest rate derivatives. In this chapter, we are going to introduce the most important interest rate models, which can be classified into two categories: short-rate and term-structure models. The short-rate models focus on the instantaneous interest rate stochastic dynamics. The rest of the term-structure is derived from the short rate at a point in time, and from the model parameters. Term-structure models, on the other hand, specify equations for (forward) interest rates in all maturities, and these equations are tied by certain consistency (non-arbitrage) conditions. In both cases, the models are developed and applied under a risk-neutral measure, but can be calibrated from the real-world data.

Date: 2020
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DOI: 10.1007/978-3-030-51751-9_7

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