Multi-regime nonlinear capital asset pricing models

A multiple-regime threshold generalized autoregressive conditionally heteroskedastic capital asset pricing model is introduced. The model captures asymmetric risk through allowing market beta to change discretely between regimes that are driven by market information. Asymmetric volatility and mean equation dynamics are also captured. We confirm the time-varying nature of market risk, in response to changes in the market, and that this discrete time variation can differ across assets. These findings could have important implications for optimizing investment decisions: e.g. in risk assessment, portfolio selection and hedging decisions.     

Relative forecasting performance of volatility models: Monte Carlo evidence

Abstract

A Monte Carlo (MC) experiment is conducted to study the forecasting performance of a variety of volatility models under alternative data-generating processes (DGPs). The models included in the MC study are the (Fractionally Integrated) Generalized Autoregressive Conditional Heteroskedasticity models ((FI)GARCH), the Stochastic Volatility model (SV), the Long Memory Stochastic Volatility model (LMSV) and the Markov-switching Multifractal model (MSM). The MC study enables us to compare the relative forecasting performance of the models accounting for different characterizations of the latent volatility process: specifications that incorporate short/long memory, autoregressive components, stochastic shocks, Markov-switching and multifractality. Forecasts are evaluated by means of mean squared errors (MSE), mean absolute errors (MAE) and value-at-risk (VaR) diagnostics. Furthermore, complementarities between models are explored via forecast combinations. The results show that (i) the MSM model best forecasts volatility under any other alternative characterization of the latent volatility process and (ii) forecast combinations provide systematic improvements upon most single misspecified models, but are typically inferior to the MSM model even if the latter is applied to data governed by other processes.     

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is particularly suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing the estimation of the VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.     

Volatility transmission patterns and terrorist attacks

The objective of this study is to analyse volatility transmission between the US and Eurozone stock markets considering the financial market responses to the September 11, March 11 and July 7 terrorist attacks. In order to do this, we use a multivariate GARCH model and take into account the asymmetric volatility phenomenon, the non-synchronous trading problem and the turmoil periods themselves. Moreover, a graphical analysis of the Asymmetric Volatility Impulse-Response Functions (AVIRF) is introduced, which takes into consideration the financial market responses to the terrorist attacks. Results suggest that there is bidirectional and asymmetric volatility transmission and show the different impacts that terrorist attacks had on both markets.     

Volatility linkages of the equity,bond and money markets: an implied volatility approach

This study proposes an alternative approach for examining volatility linkages between Standard & Poor's 500, Eurodollar futures and 30 year Treasury Bond futures markets using implied volatility from the three markets. Simple correlation analysis between implied volatilities in the three markets is used to assess market correlations. Spurious correlation effects are considered and controlled for. I find that correlations between implied volatilities in the equity, money and bond markets are positive, strong and robust. Furthermore, I replicate the approach of Fleming, Kirby and Ostdiek (1998) to check the substitutability of the implied volatility approach and find that the results are nearly identical; I conclude that my approach is simple, robust and preferable in practice. I also argue that the results from this paper provide supportive evidence on the information content of implied volatilities in the equity, bond and money markets.     

Forecasting implied volatility in foreign exchange markets: a functional time series approach

We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; Euro/United States Dollar, Euro/British Pound, and Euro/Japanese Yen. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006–2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.     

On a subjective approach to risk measurement

This study is based on the analogy between hedging a risky asset and keeping reserves to meet an unknown demand. The optimal hedging level, which depends on individual preferences, is regarded as a measure of risk. We determine the set of optimal levels and investigate the properties of the associated risk measures. This approach provides a new insight into Value at Risk (VaR). We consider it as a solution of a certain optimal inventory problem with linear cost and loss functions. We show that these functions determine the confidence level of VaR. In this way we obtain a simple model that helps us to choose a proper confidence level α and explains why supervisory institutions (such as the Basle Committee) choose a higher α than financial institutions themselves.     

Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models

We present a neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models—including second-generation stochastic volatility models and the rough volatility family—and a range of derivative contracts. Neural networks in this work are used in an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. The form in which information from available data is extracted and used influences network performance: The grid-based algorithm used for calibration is inspired by representing the implied volatility and option prices as a collection of pixels. We highlight how this perspective opens new horizons for quantitative modelling. The calibration bottleneck posed by a slow pricing of derivative contracts is lifted, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. We demonstrate the calibration performance both on simulated and historical data, on different derivative contracts and on a number of example models of increasing complexity, and also showcase some of the potentials of this approach towards model recognition. The algorithm and examples are provided in the Github repository GitHub: NN-StochVol-Calibrations.     

Portfolio frontiers with restrictions to tracking error volatility and value at risk

Asset managers are often given the task of restricting their activity by keeping both the value at risk (VaR) and the tracking error volatility (TEV) under control. However, these constraints may be impossible to satisfy simultaneously because VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performance and produces a wide variety of scenarios in the risk-return space. The aim of this paper is to analyse various interactions between portfolio frontiers when risk managers impose joint restrictions upon TEV and VaR. Specifically, we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available. Finally, we introduce a new portfolio frontier.     

A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback

Recent market events have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a trade arrival model with variable size orders and a general arrival-time distribution. With simplifications we are led in the jump-free case to a local volatility model defined by a hybrid SDE mixing both arithmetic and geometric or CIR Brownian motions, whose solution in the geometric case is given by a class of integrals of exponentials of one Brownian motion against another, in forms considered by Yor and collaborators. The reduction of the hybrid SDE to a single Brownian motion leads to an SDE of the form considered by Nagahara, which is a type of ‘Pearson diffusion’, or, equivalently, a hyperbolic OU SDE. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Student or Pearson Type~IV form. Under less-restrictive assumptions, richer dynamics are possible, including time-dependent Johnson-SU distributions and bimodal structures. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ‘25σ’ events are significantly more probable. We exhibit simple example solutions of the Fokker–Planck equation that shows how such variance explosion can hide beneath a standard Gaussian facade. These are elementary members of an extended class of distributions with a rich and varied structure, capable of describing a wide range of market behaviors. Several approaches to the density function are possible, and an example of the computation of a hyperbolic VaR is given. The model also suggests generalizations of the Bougerol identity. We touch briefly on the extent to which such a model is consistent with the dynamics of a ‘flash-crash’ event, and briefly explore the statistical evidence for our model.     

Transitional credit modelling and its relationship to market value at risk: an Australian sectoral perspective

Internal credit risk modelling is important for banks for the calculation of capital adequacy in terms of the Basel Accords, and for the management of sectoral exposure. We examine Credit Value at Risk (VaR), Conditional Credit Value at Risk (Credit CVaR) and the relationship between market and credit risk. Significant association is found between different Credit CVaR methods, and between market and credit risk. Simpler Credit CVaR methods are found to be viable alternatives to more complex methodology. The relationship between market and credit risk is used to develop a new model that allows banks to incorporate industry risk into transition modelling, without macroeconomic analysis.