Essays on fixed Income, variance risk premium, and target based optimal portfolio

This Ph.D. thesis consists of three research papers, each one contained in a separate Chapter, that are linked by one common subject: innovations in Fixed Income instruments. This preface introduces the content of the three chapters and briefly explains how the research questions have been addressed. The first chapter of this thesis provides an introduction to the topic and the instruments. In particular, we will review the literature for bonds and related portfolio problem while later we will look at Credit Default Swap (CDS) and related payoff description. The second chapter proposes a method for quantifying the variance risk premium in the credit market. We derive theoretically and we show numerically that the riskneutral expected value of the return variance can be inferred from the market prices of the credit index options. The variance risk premium is defined as the difference between the realized variance and the synthetic simple variance swap rate. Using a novel data set, we synthesize the risk neutral variance and we empirically test the historical variance risk premia magnitude on three European Credit Default Swap Indices. The study in Chapter 3 aims to bridge the gap in the existing literature identified in Chapter 1 the context of fixed income portfolio optimization. Specifically, the paper in Chapter 3, which is jointly written with Francesco Menoncin derives a closed-form solution to the optimal investment target problem. We show that the target problem is equivalent to the mean-variance one. We model the bond market using a Dynamic Nelson-Siegel-Svensson model starting from the yield to maturity curve that can lead to an incomplete market representation. Finally, we have presented numerical result of the optimal portfolio dynamics.