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When Risks and Uncertainties Collide: Mathematical Finance for Arbitrage Markets in a Quantum Mechanical ViewJun 15 2019Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting ... More
Stochastic PDEs for large portfolios with general mean-reverting volatility processesJun 13 2019In this article we consider a large structural market model of defaultable assets, where the asset value processes are modelled by using stochastic volatility models with default upon hitting a lower boundary. The volatility processes are picked from ... More
Neural Learning of Online Consumer Credit RiskJun 05 2019This paper takes a deep learning approach to understand consumer credit risk when e-commerce platforms issue unsecured credit to finance customers' purchase. The "NeuCredit" model can capture both serial dependences in multi-dimensional time series data ... More
Fair Pricing of Variable Annuities with Guarantees under the Benchmark ApproachJun 04 2019In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and ... More
Two Resolutions of the Margin Loan Pricing PuzzleJun 03 2019This paper supplies two possible resolutions of Fortune's (2000) margin-loan pricing puzzle. Fortune (2000) noted that the margin loan interest rates charged by stock brokers are very high in relation to the actual (low) credit risk and the cost of funds. ... More
The Laws of Motion of the Broker Call Rate in the United StatesJun 03 2019In this paper, which is the third installment of the author's trilogy on margin loan pricing, we analyze $1,367$ monthly observations of the U.S. broker call money rate, which is the interest rate at which stock brokers can borrow to fund their margin ... More
Portfolio diversification based on ratios of risk measuresJun 03 2019A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately ... More
Portfolio diversification based on ratios of risk measuresJun 03 2019Jun 05 2019A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance theory and other known portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality and ultimately ... More
Understanding Distributional Ambiguity via Non-robust Chance ConstraintJun 03 2019The choice of the ambiguity radius is critical when an investor uses the distributionally robust approach to address the issue that the portfolio optimization problem is sensitive to the uncertainties of the asset return distribution. It cannot be set ... More
Optimal Dynamic Strategies on Gaussian ReturnsMay 31 2019Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters ... More
The Network Effect in Credit Concentration RiskMay 31 2019Measurement and management of credit concentration risk is critical for banks and relevant for micro-prudential requirements. While several methods exist for measuring credit concentration risk within institutions, the systemic effect of different institutions' ... More
Cross-sectional Learning of Extremal Dependence among Financial AssetsMay 31 2019We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random ... More
An assets-liabilities dynamical model of banking system and systemic risk governanceMay 29 2019We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the difference between ... More
How big should a Stress Shock be?May 24 2019Stress shocks are often calculated as multiples of the standard deviation of a history set. This paper investigates how many standard deviations are required to guarantee that this shock exceeds any observation within the history set, given the additional ... More
Real-time Prediction of Bitcoin bubble CrashesMay 23 2019In the past decade, Bitcoin has become an emerging asset class well known to most people because of their extraordinary return potential in phases of extreme price growth and their unpredictable massive crashes. We apply the LPPLS confidence indicator ... More
Variable annuities in a Lévy-based hybrid model with surrender riskMay 23 2019This paper proposes a market consistent valuation framework for variable annuities with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous ... More
Testing Sharpe ratio: luck or skill?May 20 2019May 21 2019Sharpe ratio (sometimes also referred to as information ratio) is widely used in asset management to compare and benchmark funds and asset managers. It computes the ratio of the (excess) net return over the strategy standard deviation. However, the elements ... More
Spectral risk measures and uncertaintyMay 19 2019Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we propose a Deviation-based ... More
What is the Minimal Systemic Risk in Financial Exposure Networks?May 15 2019Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic ... More
Reduced Form Capital OptimizationMay 15 2019We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form ... More
ERRATUM: Stochastic evolution equations for large portfolios of stochastic volatility modelsMay 10 2019In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then we redevelop ... More
Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationMay 01 2019We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers ... More
Avoiding Backtesting Overfitting by Covariance-Penalties: an empirical investigation of the ordinary and total least squares casesMay 01 2019Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt ... More
Risk measures and progressive enlargement of filtration: a BSDE approachApr 30 2019We consider dynamic risk measures induced by Backward Stochastic Differential Equations (BSDE) in enlargement of filtration setting. On a fixed probability space, we are given a standard Brownian motion and a pair of random variables $(\tau, \zeta) \in ... More
Tail models and the statistical limit of accuracy in risk assessmentApr 27 2019In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is unknown, the database ... More
Optimal investment strategy for DC pension plans with stochastic force of mortalityApr 23 2019This paper studies an optimal portfolio problem for a DC pension plan considering both interest rate risk and longevity risk. In the accumulation phase, plan members pay constant contributions continuously into the pension fund. We assume that the evolution ... More
Simulation-based Value-at-Risk for Nonlinear PortfoliosApr 19 2019Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially ... More
The Black-Scholes Equation in Presence of ArbitrageApr 17 2019We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove ... More
Loss-based risk statistics with set-valued analysisApr 16 2019Since the portfolio has become a hot topic, we wii introduce a special risk statistics from the perspective of loss. This new risk statistic can be uesd for the quantification of portfolio risk. Representation results are provided. Finally, examples are ... More
Loss-based risk statistics with scenario analysisApr 16 2019Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension ... More
Cash sub-additive risk statistics with scenario analysisApr 16 2019Since the money is of time value, we will study a new class of risk statistics, named cash sub-additive risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, ... More
Tail probabilities of random linear functions of regularly varying random vectorsApr 15 2019We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random ... More
Deep Generative Models for Reject Inference in Credit ScoringApr 12 2019Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this ... More
Optimal excess-of-loss reinsurance for stochastic factor risk modelsApr 10 2019We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked ... More
A Thermodynamic Picture of Financial Market and Model RiskMar 30 2019By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty ... More
Portfolio optimization with two coherent risk measuresMar 25 2019We provide a closed-form analytical solution to a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio ... More
A Machine Learning approach to Risk Minimisation in Electricity Markets with Coregionalized Sparse Gaussian ProcessesMar 22 2019The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining ... More
A Machine Learning approach to Risk Minimisation in Electricity Markets with Coregionalized Sparse Gaussian ProcessesMar 22 2019Apr 03 2019The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining ... More
Computation of systemic risk measures: a mixed-integer linear programming approachMar 20 2019Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures ... More
Risk and Return models for Equity Markets and Implied Equity Risk PremiumMar 18 2019Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating ... More
Optimal FX Hedge Tenor with Liquidity RiskMar 15 2019We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged ... More
Machine Learning Risk ModelsMar 15 2019We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning ... More
Machine Learning Risk ModelsMar 15 2019Apr 09 2019We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning ... More
A lending scheme for a system of interconnected banks with probabilistic constraints of failureMar 14 2019We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of a bank. The solution can be applied to a network of banks providing a general solution when aforementioned probability ... More
Altcoin-Bitcoin ArbitrageMar 13 2019Apr 02 2019We give an algorithm and source code for a cryptoasset statistical arbitrage alpha based on a mean-reversion effect driven by the leading momentum factor in cryptoasset returns discussed in https://ssrn.com/abstract=3245641. Using empirical data, we identify ... More
Altcoin-Bitcoin ArbitrageMar 13 2019We give an algorithm and source code for a cryptoasset statistical arbitrage alpha based on a mean-reversion effect driven by the leading momentum factor in cryptoasset returns discussed in https://ssrn.com/abstract=3245641. Using empirical data, we identify ... More
Nonlinear expectations of random setsMar 12 2019Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions ... More
Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its SourceMar 10 2019Since the introduction of risk-based solvency regulation, pro-cyclicality has been a subject of concerns from all market participants. Here, we lay down a methodology to evaluate the amount of pro-cyclicality in the way financial institutions measure ... More
On occupation times in the red of Lévy risk modelsMar 09 2019In this paper, we complement the existing literature on the occupation time in the red (below level $0$) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative L\'evy process. For both classes of processes, ... More
Kernel Based Estimation of Spectral Risk MeasuresMar 08 2019Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimator for the class of spectral risk measures (SRMs) has the form of $L$-statistics. In the literature, various authors have studied and derived the asymptotic ... More
Fair Capital Risk AllocationFeb 26 2019In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular ... More
Statistical arbitrage of coherent risk measuresFeb 26 2019We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability if the market admits statistical arbitrage opportunities which we term $\rho$-arbitrage for a risk measure $\rho$. We show how to determine ... More
Controlling systemic risk - network structures that minimize it and node properties to calculate itFeb 22 2019Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk evaluation which requires ... More
Revising SA-CCRFeb 22 2019Apr 08 2019From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market Model
From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market ModelFeb 22 2019SA-CCR has major issues including: lack of self-consistency for linear trades; lack of appropriate risk sensitivity (zero positions can have material add-ons; moneyness is ignored); dependence on economically-equivalent confirmations. We show that SA-CCR ... More
Risk Management with Tail Conditional Certainty EquivalentsFeb 19 2019Certainty Equivalent is a utility-based measure that performs as a measure in which investors are indifferent between this measure and investment that holds some uncertainty. Therefore, it plays an essential role in utility-based decision making. One ... More
Risk management with machine-learning-based algorithmsFeb 14 2019We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies ... More
Risk management with machine-learning-based algorithmsFeb 14 2019Feb 25 2019We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms resulting strategies ... More
Elicitability of Range Value at RiskFeb 12 2019The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring functions should be (strictly) consistent for ... More
Elicitability of Range Value at RiskFeb 12 2019Mar 26 2019The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring function should be (strictly) consistent for the ... More
Modelling Extremal Dependence for Operational Risk by a Bipartite GraphFeb 08 2019We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails ... More
Multivariate risk measures in the non-convex settingFeb 02 2019The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite number of transfers ... More
Asymptotic approximation of the probability of ruin for large values of the Poisson rateFeb 02 2019We analyze the probability of ruin for the {\it scaled} classical Cramer-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart (1969) to the actuarial literature, amounts to multiplying the Poisson ... More
A copula based Markov Reward approach to the credit spread in European UnionFeb 02 2019In this paper, we propose a methodology based on piece-wise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial ... More
Erratum: Higher Order Elicitability and Osband's PrincipleJan 25 2019This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
Psychological model of the investor and manager behavior in riskJan 25 2019All people have to make risky decisions in everyday life. And we do not know how true they are. But is it possible to mathematically assess the correctness of our choice? This article discusses the model of decision making under risk on the example of ... More
Systemic Risk: Conditional Distortion Risk MeasuresJan 15 2019Jan 28 2019In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known ... More
Dynamic Tail Inference with Log-Laplace VolatilityJan 08 2019Feb 26 2019We propose a family of stochastic volatility models that enable predictive estimation of time-varying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally log-Laplace ... More
Dynamic Tail Inference with Log-Laplace VolatilityJan 08 2019Feb 05 2019We propose a family of stochastic volatility models that enable direct estimation of time-varying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally log-Laplace ... More
Dynamic Tail Inference with Log-Laplace VolatilityJan 08 2019Mar 28 2019We propose a family of stochastic volatility models that enable predictive estimation of time-varying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally log-Laplace ... More
Multimodal deep learning for short-term stock volatility predictionDec 25 2018Stock market volatility forecasting is a task relevant to assessing market risk. We investigate the interaction between news and prices for the one-day-ahead volatility prediction using state-of-the-art deep learning approaches. The proposed models are ... More
An Enhanced Initial Margin Methodology to Manage Warehoused Credit RiskDec 21 2018The use of CVA to cover credit risk is widely spread, but has its limitations. Namely, dealers face the problem of the illiquidity of instruments used for hedging it, hence forced to warehouse credit risk. As a result, dealers tend to offer a limited ... More
An optimization approach to adaptive multi-dimensional capital managementDec 20 2018Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business ... More
Network Effects and Default Clustering for Large PortfoliosDec 18 2018We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution ... More
Network effects in default clustering for large systemsDec 18 2018May 30 2019We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution ... More
Portfolio Rebalancing under Uncertainty Using Meta-heuristic AlgorithmDec 18 2018In this paper, we solve portfolio rebalancing problem when security returns are represented by uncertain variables considering transaction costs. The performance of the proposed model is studied using constant-proportion portfolio insurance (CPPI) as ... More
Systemic risk governance in a dynamical model of a banking systemDec 17 2018We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary reserves of the ... More
Can Deep Learning Predict Risky Retail Investors? A Case Study in Financial Risk Behavior ForecastingDec 14 2018Jan 17 2019The success of deep learning for unstructured data analysis is well documented but little evidence has emerged related to the structured, tabular datasets used in decision support. We address this research gap by considering the potential of deep learning ... More
Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfoliosDec 14 2018Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ be independent Bernoulli random variables independent ... More
Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfoliosDec 14 2018Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{\lambda_i}$'s, with ${\rm ... More
Infinitesimal perturbation analysis for risk measures based on the Smith max-stable random fieldDec 14 2018When using risk or dependence measures based on a given underlying model, it is essential to be able to quantify the sensitivity or robustness of these measures with respect to the model parameters. In this paper, we consider an underlying model which ... More
Weak comonotonicityDec 12 2018The classical notion of comonotonicity has played a pivotal role when solving diverse problems in economics, finance, and insurance. In various practical problems, however, this notion of extreme positive dependence structure is overly restrictive and ... More
Monetary Measures of RiskDec 11 2018This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal ways to construct ... More
Modelling China's Credit System with Complex Network Theory for Systematic Credit Risk ControlDec 04 2018The insufficient understanding of the credit network structure was recognized as a key factor for regulators' underestimation of the destructive systematic risk during the financial crisis that started in 2007. The existing credit network research either ... More
Optimal Resource Allocation over Networks via Lottery-Based MechanismsDec 03 2018We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called ... More
Systemic risk measures with markets volatilityNov 30 2018Jan 04 2019As systemic risk has become a hot topic in the financial markets, how to measure, allocate and regulate the systemic risk are becoming especially important. However, the financial markets are becoming more and more complicate, which makes the usual study ... More
Swimming with Wealthy Sharks: Longevity, Volatility and the Value of Risk PoolingNov 28 2018Who {\em values} life annuities more? Is it the healthy retiree who expects to live long and might become a centenarian, or is the unhealthy retiree with a short life expectancy more likely to appreciate the pooling of longevity risk? What if the unhealthy ... More
Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density EstimationNov 27 2018Feb 17 2019Conditional 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) ... More
Robust Classification of Financial RiskNov 27 2018Algorithms are increasingly common components of high-impact decision-making, and a growing body of literature on adversarial examples in laboratory settings indicates that standard machine learning models are not robust. This suggests that real-world ... More
Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk SharingNov 22 2018Dec 11 2018In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive ... More
Fast mean-reversion asymptotics for large portfolios of stochastic volatility modelsNov 21 2018We consider a large portfolio limit where the asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier. When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit ... More
A sparse grid approach to balance sheet risk measurementNov 21 2018In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that ... More
The value of forecasts: Quantifying the economic gains of accurate quarter-hourly electricity price forecastsNov 21 2018We propose a multivariate elastic net regression forecast model for German quarter-hourly electricity spot markets. While the literature is diverse on day-ahead prediction approaches, both the intraday continuous and intraday call-auction prices have ... More
An analysis of cryptocurrencies conditional cross correlationsNov 20 2018Feb 26 2019This letter explores the behavior of conditional correlations among main cryptocurrencies, stock and bond indices, and gold, using a generalized DCC class model. From a portfolio management point of view, asset correlation is a key metric in order to ... More
Entropy and Transfer Entropy: The Dow Jones and the build up to the 1997 Asian CrisisNov 20 2018Entropy measures in their various incarnations play an important role in the study of stochastic time series providing important insights into both the correlative and the causative structure of the stochastic relationships between the individual components ... More
Arbitrage Opportunities in CDS Term Structure: Theory and Implications for OTC DerivativesNov 20 2018Dec 16 2018Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of corporate and ... More
On approximations of Value at Risk and Expected Shortfall involving kurtosisNov 15 2018We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal ... More
Predicting Distresses using Deep Learning of Text Segments in Annual ReportsNov 13 2018Corporate distress models typically only employ the numerical financial variables in the firms' annual reports. We develop a model that employs the unstructured textual data in the reports as well, namely the auditors' reports and managements' statements. ... More
A framework for simulating systemic risk and its application to the South African banking sectorNov 10 2018We present a network-based framework for simulating systemic risk that considers shock propagation in banking systems. In particular, the framework allows the modeller to reflect a top-down framework where a shock to one bank in the system affects the ... More
A martingale concept for non-monotone information in a jump process frameworkNov 02 2018Dec 07 2018The classical concept of martingales and compensators bases on the monotony of filtrations. This paper looks at the situation where innovations can have an expiry date such that the information dynamics becomes non-monotone. By focussing on the properties ... More