Analysis of the dynamics of the contagion phenomenon between European sovereign bonds during recent episodes of financial crises.

Summary Periods of intense risk aversion often cause significant distortions in market prices and substantial losses for investors. Each episode of financial crisis shows that the movements of generalized sales on the markets have very negative consequences on the real economy. Thus, exploring the risk aversion phenomenon and the dynamics of the propagation of panic sentiment in financial markets can help to understand these periods of high volatility.In this theme report, we explore different dimensions of the risk aversion phenomenon, in the context of European sovereign bond portfolios. The yield on government bonds, quoted by traders, is thought to reflect, among other things, the risk that the Treasury will default on its debt before the bond matures. This is the sovereign risk. Financial crises usually cause an important movement of yields to higher levels. This type of correction reflects an increase in sovereign risk, and necessarily implies an increase in the cost of financing for national Treasuries. One objective of this report is therefore to provide explicit details to Treasuries on how bond yields are expected to deteriorate in periods of risk aversion.Chapter I explores sovereign risk in the context of a probabilistic model involving heavy-tailed distributions, as well as the GAS method that allows capturing the dynamics of volatility. The fit obtained with the Generalized Hyperbolic Distributions is robust, and the results suggest that our approach is particularly effective during periods marked by erratic volatility. In order to simplify, we describe the implementation of a timeless volatility estimator, meant to reflect the intrinsic volatility of each bond. This estimator suggests that the volatility grows quadratically when it is expressed as a function of the distribution function of the yield variations. In a second step we explore a bivariate version of the model. The calibration is robust and highlights the correlations between each bond. As a general observation, our analysis confirms that tails distributions are quite appropriate for the exploration of market prices during a financial crisis.Chapter II explores different ways to exploit our probabilistic model. In order to identify the dynamics of contagion between sovereign bonds, we analyze the expected market response to a series of financial shocks. We consider an important level of granularity in terms of the severity of the underlying shock, and this allows us to identify empirical laws that are assumed to generalize the behavior of market action when risk aversion increases. We then incorporate our volatility and market action estimators to some recognized portfolio optimization approaches and we note an improvement in portfolio resilience in this new version. Finally, we develop a new portfolio optimization methodology based on the mean-reversion principle.Chapter III is dedicated to the pricing of interest rate derivatives. We now consider that risk aversion causes the emergence of discontinuities in market prices, which we simulate through jump processes. Our model focuses on Hawkes processes which have the advantage of capturing the presence of self-excitation in volatility. We develop a calibration procedure that differs from the usual procedures. The implied volatility results are consistent with the realized volatility, and suggest that the risk premium coefficients have been successfully estimated.