A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

Essays in Macroeconomics

The dissertation consists of four papers that aim at providing new contributions in the field of macroeconomics, monetary policy and financial stability. The first paper proposes a new Dynamic Stochastic General Equilibrium (DSGE) model with credit frictions and a banking sector to study the pro-cyclicality of credit and the role of different prudential regulatory frameworks in affecting business cycle fluctuations and in restoring macroeconomic and financial stability. The second paper develops a simple DSGE model capable of evaluating the effects of large purchases of treasuries by central banks. This theoretical framework is employed to evaluate the impact on yields and the macroeconomy of large purchases of medium- and long-term government bonds recently implemented in the US and UK. The third paper studies the effects of ECB communications about unconventional monetary policy operations on the perceived sovereign risk of Italy over the last five years. The empirical results are derived from both an event-study analysis and a GARCH model, which uses Italian long-term bond futures to disentangle expected from unexpected policy actions. The fourth paper proposes a DSGE model with an endogenous term structure of interest rates, which is able to replicate the stylized facts regarding the yield curve and the term premium in the US over the period 1987:3-2011:3, without compromising its ability to match macro dynamics.

Essays in Macroecometrics: methodological aspects and empirical applications

In the first chapter, I develop a panel no-cointegration test which extends Pesaran, Shin and Smith (2001)'s bounds test to the panel framework by considering the individual regressions in a Seemingly Unrelated Regression (SUR) system. This allows to take into account unobserved common factors that contemporaneously affect all the units of the panel and provides, at the same time, unit-specific test statistics. Moreover, the approach is particularly suited when the number of individuals of the panel is small relatively to the number of time series observations. I develop the algorithm to implement the test and I use Monte Carlo simulation to analyze the properties of the test. The small sample properties of the test are remarkable, compared to its single equation counterpart. I illustrate the use of the test through a test of Purchasing Power Parity in a panel of EU15 countries. In the second chapter of my PhD thesis, I verify the Expectation Hypothesis of the Term Structure in the repurchasing agreements (repo) market with a new testing approach. I consider an "inexact" formulation of the EHTS, which models a time-varying component in the risk premia and I treat the interest rates as a non-stationary cointegrated system. The effect of the heteroskedasticity is controlled by means of testing procedures (bootstrap and heteroskedasticity correction) which are robust to variance and covariance shifts over time. I fi#nd that the long-run implications of EHTS are verified. A rolling window analysis clarifies that the EHTS is only rejected in periods of turbulence of #financial markets. The third chapter introduces the Stata command "bootrank" which implements the bootstrap likelihood ratio rank test algorithm developed by Cavaliere et al. (2012). The command is illustrated through an empirical application on the term structure of interest rates in the US.

Real effects of the IFRS 9 adoption in banking

The recent adoption of IFRS 9 is a highly disruptive accounting reform, with significant impacts on how and when negative news (i.e., negative adjustments to reported earnings) are recognized on the financial statements. Using a unique dataset of two major banks operating in one European country we provide evidence of a tightening of the corporate loans pricing after the IFRS 9 adoption. Furthermore, by focusing on the post reform period, we show that the tightening is driven by the new staging classification. Higher risk premiums are associated to clients with previous underperforming exposures (stage 2) and higher probability of default. We also observe that the staging classification is not affecting climate risk premiums. Our results highlight that the lenders, as expected by the regulation, change their risk appetite by charging higher spreads to discourage loan origination for clients that became too risky and expensive under the new standard.