Higher moment models for risk and portfolio management

This thesis considers specific topics related to the dynamic modelling and management of risk, with a particular emphasis on the generation of asymmetric and fat tailed behavior observed in practise. Specifically, extensions to the dynamics of the popular GARCH model, to capture time variation in higher moments, are considered in the univariate and multivariate context, with a special focus on the Generalized Hyperbolic distribution. In Chapter 1, I consider the extension of univariate GARCH processes with higher moment dynamics based on the Autoregressive Conditional Density model of Hansen (1994), with conditional distribution the Generalized Hyperbolic. The value of such dynamics are analyzed in the context of risk management, and the question of ignoring them discussed. In Chapter 2, I review some popular multivariate GARCH models with a particular emphasis on the dynamic correlation model of Engle (2002), and alternative distributions such those from the Generalized Asymmetric Laplace of Kotz, Kozubowski, and Podgorski (2001). In Chapter 3, I propose a multivariate extension to the Autoregressive Conditional Density model via the independence framework of the Generalized Orthogonal GARCH models, providing the first feasible model for large dimensional multivariate modelling of time varying higher moments. A comprehensive out-of- sample risk and portfolio management application provides strong evidence of the improvement over non time varying higher moments. Finally, in Chapter 4, I consider the benefits of active investing when the benchmark index is not optimally weighted. I investigate advances in the definition and use of risk measures in portfolio allocation, and propose certain simple solutions to challenges arising in the optimization of these measures. Combining the models discussed in the previous chapters, within a fractional programming optimization framework and using a range of popular risk measures, a large scale out-of-sample portfolio application on the point in time constituents of the Dow Jones Industrial Average is presented and discussed, with clear implications for active investing and benchmark policy choice

Higher moment models for risk and portfolio management

This thesis considers specific topics related to the dynamic modelling and management of risk, with a particular emphasis on the generation of asymmetric and fat tailed behavior observed in practise. Specifically, extensions to the dynamics of the popular GARCH model, to capture time variation in higher moments, are considered in the univariate and multivariate context, with a special focus on the Generalized Hyperbolic distribution. In Chapter 1, I consider the extension of univariate GARCH processes with higher moment dynamics based on the Autoregressive Conditional Density model of Hansen (1994), with conditional distribution the Generalized Hyperbolic. The value of such dynamics are analyzed in the context of risk management, and the question of ignoring them discussed. In Chapter 2, I review some popular multivariate GARCH models with a particular emphasis on the dynamic correlation model of Engle (2002), and alternative distributions such those from the Generalized Asymmetric Laplace of Kotz, Kozubowski, and Podgorski (2001). In Chapter 3, I propose a multivariate extension to the Autoregressive Conditional Density model via the independence framework of the Generalized Orthogonal GARCH models, providing the first feasible model for large dimensional multivariate modelling of time varying higher moments. A comprehensive out-of- sample risk and portfolio management application provides strong evidence of the improvement over non time varying higher moments. Finally, in Chapter 4, I consider the benefits of active investing when the benchmark index is not optimally weighted. I investigate advances in the definition and use of risk measures in portfolio allocation, and propose certain simple solutions to challenges arising in the optimization of these measures. Combining the models discussed in the previous chapters, within a fractional programming optimization framework and using a range of popular risk measures, a large scale out-of-sample portfolio application on the point in time constituents of the Dow Jones Industrial Average is presented and discussed, with clear implications for active investing and benchmark policy choice.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Independent Factor Autoregressive Conditional Density Model

In this article, we propose a novel Independent Factor Autoregressive Conditional Density (IFACD) model able to generate time-varying higher moments using an independent factor setup. Our proposed framework incorporates dynamic estimation of higher comovements and feasible portfolio representation within a non-elliptical multivariate distribution. We report an empirical application, using returns data from 14 MSCI equity index iShares for the period 1996 to 2010, and we show that the IFACD model provides superior VaR forecasts and portfolio allocations with respect to the Conditionally Heteroskedastic Independent Component Analysis of Generalized Orthogonal (CHICAGO) and DCC models

Comparing Behavioural Models Using Data from Experimental Centipede Games

The centipede game posits one of the most well-known paradoxes of backward induction in the literature of experimental game theory. Given that deviations from the unique subgame perfect Nash equilibrium generates a Pareto improvement, several theoretical models have been employed in order to rationalize this kind of behavior in this social dilemma. The available explanations range from social preferences including fairness, altruism or cooperation motives, errors in playing, inability to perform backward induction or different depths of reasoning. In the present study, we use the Blavatskyy's theoretical contribution, and relax the assumptions of Expected Utility maximization and risk-neutral attitudes, to test an alternative explanation. We compare various probabilistic decision theory models in terms of their descriptive (in-sample) and predictive (out-of-sample fit) performance, using data from experimental centipede games. We find that introducing non-Expected Utility preferences to the Quantal Response Equilibrium model, along with a nonlinear utility function, provides a better explanation compared to alternative specifications such as the Level-k or the Quantal Response Equilibrium model with altruistic motives. (JEL C72, C92, D81, D82)

Dark-Bright Soliton Bound States in a Microresonator

The recent discovery of dissipative Kerr solitons in microresonators has facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, ultrafast optics and soliton states in atomic physics

Value-at-risk forecasting of the CARBS Indices

Abstract: The purpose of this paper is to use calibrated univariate GARCH family models to forecast volatility and value at risk (VaR) of the CARBS indices and a global minimum variance portfolio (GMVP) constructed using the CARBS equity indices. the reliability of the different volatility forecasts are tested using the mean absolute error (MAE) and the mean squared error (MSE). The rolling forecast of VaR is tested using a back-testing procedure. The results indicate that the use of a rolling forecast from a GARCH model when estimating VaR for the CARBS indices and the GMVP is not a reliable method

Univariate and multivariate GARCH models applied to the CARBS indices

Abstract: The purpose of this paper is to estimate the calibrated parameters of different univariate and multivariate GARCH family models. It is unrealistic to assume that volatility of financial returns is constant. In the empirical analysis, the symmetric GARCH, and asymmetric GJR-GARCH and EGARCH models were estimated for the CARBS indices and a global minimum variance portfolio (GMVP), the best fitting model was determined using the AIC and BIC. The asymmetric terms of the GJR-GARCH and EGARCH models indicate signs of the leverage effect. The information criterion suggest that the EGARCH model is the best fitting model for the CARBS indices and the GMVP

Market risk management in a post-Basel II regulatory environment

We propose a novel method of Mean-Capital Requirement portfolio optimization. The optimization is performed using a parallel framework for optimization based on the Nondominated Sorting Genetic Algorithm II. Capital requirements for market risk include an additional stress component introduced by the recent Basel 2.5 regulation. Our optimization with the Basel 2.5 formula in the objective function produces superior results to those of the old (Basel II) formula in stress scenarios in which the correlations of asset returns change considerably. These improvements are achieved at the expense of reduced cardinality of Pareto-optimal portfolios. This reduced cardinality (and thus portfolio diversification) in periods of relatively low market volatility may have unintended consequences for banks’ risk exposure

Real-time imaging of standing-wave patterns in microresonators

Real-time characterization of microresonator dynamics is important for many applications. In particular, it is critical for near-field sensing and understanding light–matter interactions. Here, we report camera-facilitated imaging and analysis of standing wave patterns in optical ring resonators. The standing wave pattern is generated through bidirectional pumping of a microresonator, and the scattered light from the microresonator is collected by a short-wave infrared (SWIR) camera. The recorded scattering patterns are wavelength dependent, and the scattered intensity exhibits a linear relation with the circulating power within the microresonator. By modulating the relative phase between the two pump waves, we can control the generated standing waves’ movements and characterize the resonator with the SWIR camera. The visualized standing wave enables subwavelength distance measurements of scattering targets with nanometer-level accuracy. This work opens broad avenues for applications in on-chip near-field (bio)sensing, real-time characterization of photonic integrated circuits, and backscattering control in telecom systems