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Essays on the modeling of risks in interest-rate and inflation markets
This thesis considers the modelling of interest-rate and inflation-markets in four separate essays, where two of the essays are mainly theoretical and two are mainly empirical. The first essay considers the modelling of stochastic skewness in arbitrage-free term-structure models. By specifying a model which is part of the Heath-Jarrow-Morton-framework and calibrating the model to caps and floors on EURIBOR rates, we show how stochastic skewness can be modelled. The second essay considers the modelling of inflation derivatives in a Heath-Jarrow-Morton-framework with jumps and stochastic volatility. The model allows for pricing through standard numerical methods, e.g. numerical integration. Furthermore we show how the model improves the fit to data compared to a Gaussian model. The third essay considers estimation of inflation risk premia. By using data on nominal interest-rates, inflation swaps, a consumer price index and surveys on inflation expectations, we estimate an arbitrage-free model. We show that inflation risk premia are moderate, with an average 1-year inflation risk premia of 18 basis points and an average 10-year inflation risk premia of 43 basis points. Finally, we find indications that inflation risk premia related to yields with more than five years to maturity are driven by GDP-growth expectations. The fourth essay considers a test of term-structure models with a risk management perspective. The essay contains a comparative study of 6 so-called affine Nelson-Siegel models and a 2-factor Cox-Ingersoll-Ross model. The analysis shows that the simulation-horizon has an impact on the optimal choice of model, and generally a suite of models, rather than a single model, should be used.