Essays on the term structure of interest rates

This PhD thesis contains three main chapters on macro finance, with a focus on the term structure of interest rates and the applications of state-of-the-art Bayesian econometrics. Except for Chapter 1 and Chapter 5, which set out the general introduction and conclusion, each of the chapters can be considered as a standalone piece of work. In Chapter 2, we model and predict the term structure of US interest rates in a data rich environment. We allow the model dimension and parameters to change over time, accounting for model uncertainty and sudden structural changes. The proposed timevarying parameter Nelson-Siegel Dynamic Model Averaging (DMA) predicts yields better than standard benchmarks. DMA performs better since it incorporates more macro-finance information during recessions. The proposed method allows us to estimate plausible realtime term premia, whose countercyclicality weakened during the financial crisis. Chapter 3 investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in the bond yields of seven advanced economies is due to global co-movement. Our results suggest that global inflation is the most important factor among global macro fundamentals. Non-fundamental factors are essential in driving global co-movements, and are closely related to sentiment and economic uncertainty. Lastly, we analyze asymmetric spillovers in global bond markets connected to diverging monetary policies. Chapter 4 proposes a no-arbitrage framework of term structure modeling with learning and model uncertainty. The representative agent considers parameter instability, as well as the uncertainty in learning speed and model restrictions. The empirical evidence shows that apart from observational variance, parameter instability is the dominant source of predictive variance when compared with uncertainty in learning speed or model restrictions. When accounting for ambiguity aversion, the out-of-sample predictability of excess returns implied by the learning model can be translated into significant and consistent economic gains over the Expectations Hypothesis benchmark.

Essays on the term structure of interest rates

This PhD thesis contains three main chapters on macro finance, with a focus on the term structure of interest rates and the applications of state-of-the-art Bayesian econometrics. Except for Chapter 1 and Chapter 5, which set out the general introduction and conclusion, each of the chapters can be considered as a standalone piece of work. In Chapter 2, we model and predict the term structure of US interest rates in a data rich environment. We allow the model dimension and parameters to change over time, accounting for model uncertainty and sudden structural changes. The proposed time-varying parameter Nelson-Siegel Dynamic Model Averaging (DMA) predicts yields better than standard benchmarks. DMA performs better since it incorporates more macro-finance information during recessions. The proposed method allows us to estimate plausible real-time term premia, whose countercyclicality weakened during the financial crisis. Chapter 3 investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in the bond yields of seven advanced economies is due to global co-movement. Our results suggest that global inflation is the most important factor among global macro fundamentals. Non-fundamental factors are essential in driving global co-movements, and are closely related to sentiment and economic uncertainty. Lastly, we analyze asymmetric spillovers in global bond markets connected to diverging monetary policies. Chapter 4 proposes a no-arbitrage framework of term structure modeling with learning and model uncertainty. The representative agent considers parameter instability, as well as the uncertainty in learning speed and model restrictions. The empirical evidence shows that apart from observational variance, parameter instability is the dominant source of predictive variance when compared with uncertainty in learning speed or model restrictions. When accounting for ambiguity aversion, the out-of-sample predictability of excess returns implied by the learning model can be translated into significant and consistent economic gains over the Expectations Hypothesis benchmark.

Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.