The purpose of this advanced-level seminar is to give you a good and practical understanding of modern interest rate models and their uses in option pricing and risk management.
We first present and explain important concepts such as the term structure of interest rates and the term structure of volatility. We then take a closer look at various processes for interest rate evolvement over time, and we explain how interest rate volatility and "mean reversion" can be modelled into these processes.
Next, we present and explain widely used "equilibrium" models such as the Vasicek and Cox-Ingersoll-Ross models. We explain the general forms of these models and demonstrate how they can be estimated and used for simulating interest rate processes and for constructing yield curves. We also discuss how these models can be extended to multi-factor models such as the Brennan-Schwarz model.
We then turn our focus to look at "no-arbitrage" models. This class of models includes models such as the Ho-Lee, Vasicek, Hull-White and the Black-Derman-Toy models. We also present the popular "Swap Market" and "Libor Market" (BGM) model, which are widely used by practitioners. We discuss the important characteristics and parameters of these models, and we demonstrate how they can be constructed, calibrated and used under the double-curve framework which was introduced following the liquidity crisis that started in the summer 2007. We revisit the problem of pricing and hedging plain vanilla single currency interest rate derivatives using different yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. We also derive the no arbitrage double curve market-like formulas for basic plain vanilla interest rate derivatives and show how they can be used for pricing of FRA, swaps, cap/floors and swaptions etc.
Further, we present models for stochastic volatility, exemplified by the widely used Heston Model today. We motivate the uses of such models, and we show how the model is computationally validated, calibrated and applied in the pricing of standard and more exotic interest rate options.
Finally, we look at how interest rate models can be used for various risk management purposes, including calculating key ratios and estimating return distributions for "Value-at-Risk" calculation.