Quantitative Finance

The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is developed and employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH, GARCH with two-sided Weibull distribution and realized GARCH models, tail risk forecasting results across 7 market index return series and 2 individual assets clearly favor the realized GARCH models incorporating two-sided Weibull distribution, especially models employing the sub-sampled realized variance and sub-sampled realized range, over a six year period that includes the global financial crisis.

A new model framework called Realized Conditional Autoregressive Expectile (Realized-CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the Realized-GARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed as the dependent variable in the measurement equation and to drive expectile dynamics. The measurement equation here models the contemporaneous dependence between the realized measure and the latent conditional expectile. We also propose employing the quantile loss function as the target criterion, instead of the conventional violation rate, during the expectile level grid search. For the proposed model, the usual search procedure and asymmetric least squares (ALS) optimization to estimate the expectile level and CARE parameters proves challenging and often fails to convergence. We incorporate a fast random walk Metropolis stochastic search method, combined with a more targeted grid search procedure, to allow reasonably fast and improved accuracy in estimation of this level and the associated model parameters. Given the convergence issue, Bayesian adaptive Markov Chain Monte Carlo methods are proposed for estimation, whilst their properties are assessed and compared with ALS via a simulation study. In a real forecasting study applied to 7 market indices and 2 individual asset returns, compared to the original CARE, the parametric GARCH and Realized-GARCH models, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed Realized-CARE model, especially when incorporating the Realized Range and the sub-sampled Realized Range as the realized measure in the model.

A key challenge for Bitcoin cryptocurrency holders, such as startups using ICOs to raise funding, is managing their FX risk. Specifically, a misinformed decision to convert Bitcoin to fiat currency could, by itself, cost USD millions. In contrast to financial exchanges, Blockchain based crypto-currencies expose the entire transaction history to the public. By processing all transactions, we model the network with a high fidelity graph so that it is possible to characterize how the flow of information in the network evolves over time. We demonstrate how this data representation permits a new form of microstructure modeling - with the emphasis on the topological network structures to study the role of users, entities and their interactions in formation and dynamics of crypto-currency investment risk. In particular, we identify certain sub-graphs ('chainlets') that exhibit predictive influence on Bitcoin price and volatility, and characterize the types of chainlets that signify extreme losses.

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bonus-malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus-malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.

For a risk vector V , whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the components of V and arbitrary dependence structure in a multivariate regular variation setting. Upper and lower bounds are given by asymptotically independent and fully dependent components of V with respect to the tail index α being smaller or larger than 1. Counterexamples, where for non-linear aggregation functions no bounds are available, complete the picture.

We applied the Johansen-Ledoit-Sornette (JLS) model to detect possible bubbles and crashes related to the Brexit/Bremain referendum scheduled for 23rd June 2016. Our implementation includes an enhanced model calibration using Genetic Algorithms. We selected a few historical financial series sensitive to the Brexit/Bremain scenario, representative of multiple asset classes. We found that equity and currency asset classes show no bubble signals, while rates, credit and real estate show super-exponential behaviour and instabilities typical of bubble regime. Our study suggests that, under the JLS model, equity and currency markets do not expect crashes or sharp rises following the referendum results. Instead, rates and credit markets consider the referendum a risky event, expecting either a Bremain scenario or a Brexit scenario edulcorated by central banks intervention. In the case of real estate, a crash is expected, but its relationship with the referendum results is unclear.

Interest-rate risk is a key factor for property-casualty insurer capital. P&C companies tend to be highly leveraged, with bond holdings much greater than capital. For GAAP capital, bonds are marked to market but liabilities are not, so shifts in the yield curve can have a significant impact on capital. Yield-curve scenario generators are one approach to quantifying this risk. They produce many future simulated evolutions of the yield curve, which can be used to quantify the probabilities of bond-value changes that would result from various maturity-mix strategies. Some of these generators are provided as black-box models where the user gets only the projected scenarios. One focus of this paper is to provide methods for testing generated scenarios from such models by comparing to known distributional properties of yield curves. P&C insurers hold bonds to maturity and manage cash-flow risk by matching asset and liability flows. Derivative pricing and stochastic volatility are of little concern over the relevant time frames. This requires different models and model testing than what is common in the broader financial markets. To complicate things further, interest rates for the last decade have not been following the patterns established in the sixty years following WWII. We are now coming out of the period of very low rates, yet are still not returning to what had been thought of as normal before that. Modeling and model testing are in an evolving state while new patterns emerge. Our analysis starts with a review of the literature on interest-rate model testing, with a P&C focus, and an update of the tests for current market behavior. We then discuss models, and use them to illustrate the fitting and testing methods. The testing discussion does not require the model-building section.

Aiming at quantifying and evaluating the regional commercial environment along with the level of economic development among cities in mainland China, the concept of China City Commercial Environment Credit Index(CEI) was first introduced and established in 2010. In this manuscript, a historical review and detailed introduction of CEI is included, followed by statistical studies. In particular, an independent statistical cross-check for the existing CEI-2012 is performed and significant factors that play the most in influential roles are discussed.

Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk. Buffered Probability of Exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distribution's. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distribution's. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In particular, we consider two: portfolio optimization and density estimation. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distribution's simultaneously. Second, we apply our formulas to parametric density estimation and propose the method of superquantile's (MOS), a simple variation of the method of moment's (MM) where moment's are replaced by superquantile's at different confidence levels. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data.

The paper examines the potential of deep learning to support decisions in financial risk management. We develop a deep learning model for predicting whether individual spread traders secure profits from future trades. This task embodies typical modeling challenges faced in risk and behavior forecasting. Conventional machine learning requires data that is representative of the feature-target relationship and relies on the often costly development, maintenance, and revision of handcrafted features. Consequently, modeling highly variable, heterogeneous patterns such as trader behavior is challenging. Deep learning promises a remedy. Learning hierarchical distributed representations of the data in an automatic manner (e.g. risk taking behavior), it uncovers generative features that determine the target (e.g., trader's profitability), avoids manual feature engineering, and is more robust toward change (e.g. dynamic market conditions). The results of employing a deep network for operational risk forecasting confirm the feature learning capability of deep learning, provide guidance on designing a suitable network architecture and demonstrate the superiority of deep learning over machine learning and rule-based benchmarks.