Credit Rationing Effects of Credit Value-at-Risk

Banks provide risky loans to firms which have superior information regarding the quality of their projects. Due to asymmetric information the banks face the risk of adverse selection. Credit Value-at-Risk (CVaR) regulation counters the problem of low quality, i.e. high risk, loans and therefore reduces the risk of the bank loan portfolio. However, CVaR regulation distorts the operation of credit markets. We show that a binding CVaR constraint introduces credit rationing and lowers social welfare. CVaR regulation also affects the operation of monetary policy

Equity, commodity and interest rate volatility derivatives

A new methodology to construct synthetic volatility derivatives is presented. The underlying asset price process is very general, since equity, commodities and interest rates are included. The focus is on volatility swaps and volatility swap options, but much more derivatives may be considered. The proposed methods optimize the conditional value at risk of the non-hedged risk, and yields both bid and ask prices, as well as optimal hedging strategies for both purchases and sales. Upper bounds for the broker capital losses under very negative scenarios are given. Numerical experiments are presented so as to illustrate the performance in practice of this new approach.Research partially supported by “Comunidad Autónoma de Madrid” (Spain, Grant S2009/ESP −1594) and “MEyC” (Spain, Grants ECO2009−14457−C04 and ECO2012−39031−C02−01)

Comparing Return-Risk and Direct Utility Maximization Portfolio Optimization Methods by ‘Certainty Equivalence Curves’

Mean-Risk portfolio optimization method proposes an efficient frontier that consists of portfolios not dominated by any portfolio. Consequently, this method reduces the choice set by excluding inefficient portfolios. Different risk measures offer different efficient frontiers, which can be interpreted as different optimal choice sets. The question is whether these different risk measures lead to significantly different efficient frontiers for the investors, and which risk measure should be used. My purpose is to present a method to assess the effect of the choice set reduction from different Return-Risk models and to answer the question presented earlier. The most important contribution of the paper is the creation of a two-dimensional space “Risk-Aversion – Certainty Equivalence (CE)” as a platform for comparisons. The curves, representing different risk-averse investors and different models, on this space are called “Certainty Equivalence Curves (CEC)”. The empirical analysis shows that the Mean-Variance method is very effective in ranking portfolios for exponential utility investors. Therefore, it is not recommended to use more complicated methods such as Mean-CVaR

Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling

Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging to address within the traditional mathematical finance framework. Since deep hedging relies on market simulation, the underlying asset price process model is crucial. However, existing literature on deep hedging often relies on traditional mathematical finance models, e.g., Brownian motion and stochastic volatility models, and discovering effective underlying asset models for deep hedging learning has been a challenge. In this study, we propose a new framework called adversarial deep hedging, inspired by adversarial learning. In this framework, a hedger and a generator, which respectively model the underlying asset process and the underlying asset process, are trained in an adversarial manner. The proposed method enables to learn a robust hedger without explicitly modeling the underlying asset process. Through numerical experiments, we demonstrate that our proposed method achieves competitive performance to models that assume explicit underlying asset processes across various real market data.Comment: 8 pages, 7 figure

Three essays on the Euro-Zone sovereign debt

My PhD thesis consists of three chapters on the Euro-Zone sovereign bond market due to the quick spread of sovereign risk in European countries. In chapter 1, we examine the European bond market efficiency by developing a mathematical programing approach, in order to measure the arbitrage size. Transaction costs may be incorporated. The obtained arbitrage measures have two interesting interpretations: On the one hand they provide the highest available arbitrage profit with respect to the price of the sold (bought) securities. On the other hand they give the minimum relative (per dollar) bid (ask) price modification leading to an arbitrage free market. Moreover, some primal problems lead to optimal arbitrage strategies (if available), while their dual problems generate proxies for the Term Structure of Interest Rates. The developed methodology permits us to implement an empirical test in the Euro-zone during the Euro crisis. Classical literature justifies the relevance of empirical analyses verifying the degree of efficiency during market turmoils. Our empirical study of the German, French and Spanish sovereign bonds markets finds that the main arbitrage opportunities come from the price differences between maturity-matched strips or “On-The-Run Premium” for zero-coupon bonds. When we remove the strips and the zero-coupon bonds the arbitrage still exists in the Spanish market. Although we cannot reject the existence of the arbitrage in European bond market, in order to provide a general pricing rule we assume that the market is efficient. In chapter 2, we propose a general pricing methodology for completing the European sovereign bond market due to the existence of unreplicable bonds such as a forthcoming jointguaranteed ’Eurobonds’. To find the optimal EMM, we introduce ’Ambiguity’ in our pricing framework to describe the underlying state probability, and we also consider the worst-case Conditional Value-at-Risk to measure the hedging risk. The minimization of the worst-case CVaR of hedging residual risk associated with an uncertain probability set is investigated. We transform the optimization problem into a convex and linear program which gives the robust bid-ask prices, the hedging portfolio and a risk neutral measure. In the numerical analysis, several synthetic sovereign bonds are created for imitating the performance of Eurobonds since it does not exist. In chapter 3, we focus on assessing the sovereign risk dependence of European sovereign bonds, based on the worst case analysis. With this analysis, we can also provide a robust optimal portfolio composed of sovereign bonds in the safe and the periphery countries. With uncertain state probability distribution, we adopt a robust Conditional Value at Risk (RCVaR) in the risk-return tradeoff analysis. The empirical results show that a default in a safe country significantly affects the default in periphery countries and the interaction of default risk among periphery countries are strikingly high. Moreover, the robust optimal portfolio performs stably even in the period with the highest risk and the weights in risky countries are significantly greater than zero, which indirectly implies an overpriced-risk in periphery countriesMi tesis doctoral consta de tres capítulos sobre el mercado de bonos soberanos de la Zona Euro. El interés del tema está justificado por la rápida propagación del riesgo soberano entre los paíıses europeos. En el capítulo 1, se analiza la efficiencia del mercado europeo de bonos mediante el desarrollo de nuevas medidas del nivel de arbitraje secuencial en los mercados de renta fija. Se pueden incorporar los costes de transacción, y las medidas propuestas son utilizadas para realizar contrastes empíricos. Las medidas de arbitraje obtenidas tienen dos interpretaciones interesantes: por un lado, proporcionan el mayor beneficio de arbitraje disponible con relación al precio de los activos vendidos (comprados). Por otro, proporcionan la variación relativa (o en tanto por uno) mínima de precios que conduce a un mercado sin arbitraje secuencial. Las medidas del nivel de arbitraje se definen a través de problemas lineales de optimización. Los problemas primales conducen a estrategias de arbitraje óptimas (si hay arbitraje), mientras que sus problemas duales generan aproximaciones de la estructura temporal de tipos de interés. La metodología desarrollada nos permite implementar un contraste empírico en la zona euro durante la crisis reciente. La literatura clásica justifica la conveniencia de los análisis empíricos que verifiquen el grado de eficiencia de los mercados en épocas convulsas. Nuestro estudio empírico de los mercados de bonos soberanos alemanes, franceses y españoles, concluye que las principales oportunidades de arbitraje provienen de las diferencias de precios entre los bonos con cupón y sus réplicas formadas con bonos de cupón cero. Cuando quitamos los bonos de cupón cero sigue habiendo arbitraje en el mercado español. Aunque no se puede rechazar la existencia del arbitraje en los mercados europeos de bonos, en el capítulo segundo se propone una metodología que permite dar una regla de valoración en mercados de (hoy por hoy hipotéticos) eurobonos. Consideramos un ambiente de ambigüedad en el que las verdaderas probabilidades de impago (default) son desconocidas con precisión, y por consiguiente las estimaciones incorporan márgenes de error. Tomamos el punto de vista de un intermediario financiero que valora teniendo en cuenta el coste de la cartera óptima de cobertura, que se calcula mediante la minimización del CVaR robusto, o CVaR bajo condiciones de ambigüedad. Éste coincide con el CVaR bajo el sistema de probabilidades más negativo para el intermediario financiero (enfoque del peor escenario). Transformamos el problema de optimización en un programa convexo (e incluso lineal) que da los precios de oferta y demanda, la cartera de cobertura y una medida de probabilidad neutral al riesgo. En una aplicación numérica/empírica creamos, valoramos y cubrimos distintos tipos de Eurobonos soberanos. En el capítulo 3 nos centramos en la evaluación de la dependencia del riesgo soberano de los bonos de la Eurozona, basada en el análisis del peor escenario. Con este estudio también podemos ofrecer una cartera de bonos soberanos óptima y robusta. La optimalidad es nuevamente determinada a través de CVaR bajo ambigüedad. El contraste empírico muestra que un problema en un país más solvente afecta signicativamente a los países periféricos. Por otra parte, la cartera óptima es estable incluso en el periodo de mayor riesgo, y los pesos de los países más arriesgados es signicativamente mayor que cero, lo que puede implicar una infravaloración de los bonos con menor solvencia (o una sobreestimación de su prima de riesgo).Programa Oficial de Doctorado en Economía de la Empresa y Métodos CuantitativosPresidente: Eliseo Navarro Arribas; Secretario: Silvia Mayoral Blaya; Vocal: Antonio Díaz Pére

Hedging US stock markets in wake of COVID-19 pandemic

The purpose of this pro gradu -study is to examine widely regarded hedging assets against S&P 500 stock index during the COVID-19 pandemic. The motivation to study these assets relies on previous literature and unique market conditions of COVID-19 pandemic for markets. Flight-to-quality is often observed during crisis periods when there is turmoil and distress in financial markets. Increased uncertainty drives investors to become more risk-averse and allocate capital in more stable asset classes. Previous literature has indicated that commodities, government bonds and bitcoin could benefit from such phenomenon. Additionally, by pre-emptively alloca-ting portfolio capital to such assets investors could possibly effectively hedge potential losses of one asset with gains on another assets. This study follows methodology introduced by Baur and McDermott (2010) to compare different assets hedging and safe-haven performance during the COVID-19 markets. Such retrospective analysis provides effective tool for this thesis to provide insight to support future investing theses during market uncertainty. The focus is to set on the United States as the largest open markets in the world with data running from 1st of January 2020 till 20th of December 2021. The data is first cleaned to represent same trading days as the New York Stock Exchange trading days, after which daily returns are presented in log-format of which bottom 1%, 5% and 10% quantiles are picked with dummy variables. Identical formulas are used for different assets to determinate the effectiveness to limit the volatility during these trading days in order to find out possible safe haven effectiveness and hedging ability. The obtained results suggest that most of the assets failed to act as safe haven asset during the COVID-19 markets. Only bonds successfully hedged stock market volatility and losses for inves-tors. When compared with previous literature this study does affirm and contradict number of previous studies. These results can be affected by number of factors such as different sample periods and methodological choices. Results do however indicate that U.S. Government bonds with different maturities did act as hedge against S&P 500 stock market index during the sample period. In addition, gold can be regarded as an effective diversifier with S&P 500 stock index

Alternative portfolio methods

Portfolio optimization in an uncertain environment has great practical value in investment decision process. But this area is highly fragmented due to fast evolution of market structure and changing investor behavior. In this dissertation, four methods are investigated/designed to explore their efficiency under different circumstances. Parametric portfolio decomposes weights by set of factors whose coefficients are uniquely determined via maximizing utility function. A robust bootstrap method is proposed to assist factor selection. If investors exhibit asymmetric aversion of tail risk, pessimistic models on Choquet utility maximization and coherent risk measures acquire superiority. A new hybrid method that inherits advantage of parameterization and tail risk minimization is designed. Mean-variance, which is optimal with elliptical return distribution, should be employed in the case of capital allocation to trading strategies. Nonparametric classifiers may enhance homogeneity of inputs before feeding the optimizer. Traditional factor portfolio can be extended to functional settings by applying FPCA to return curves sorted by factors. Diversification is always achieved by mixing with detected nonlinear components. This research contributes to existing literature on portfolio choice in three-folds: strength and weakness of each method is clarified; new models that outperform traditional approaches are developed; empirical studies are used to facilitate comparison