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preprint2017arXiv

Net Stable Funding Ratio: Impact on Funding Value Adjustment

In this paper we investigate the relationship between Funding Value Adjustment (FVA) and Net Stable Funding Ratio (NSFR). FVA is defined in a consistent way with NSFR such that the new framework of FVA monitors the costs due to keeping NSFR at an acceptable level, as well. In addition, the problem of choosing the optimal funding strategy is formulated as a shortest path problem where the proposed FVA framework is applied in the optimization process. The solution provides us with the optimal funding decisions that lead to the minimum funding cost of the transaction. We also provide numerical experiments for FVA calculation and optimization problem.

preprint2016arXiv

Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures

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

preprint2016arXiv

Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits

We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture distributions. We show that this leads to qualitatively different results on individual and system risks compared to heavy-tailed claims previously studied in the literature. By deducing conditional loss distributions we investigate the impact of stress situations on agents' and system's losses. Moreover, we present a criterion for agents to decide whether holding few objects or portfolio diversification minimizes their risks in system crisis situations.

preprint2016arXiv

Leverage and Uncertainty

Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to be used in successful management of risk, uncertainty and leverage. The author explores how uncertainty beyond risk determines consistent leverage in a simple model of the world with fat tails due to significant, not fully quantifiable and not too rare events. Among particular technical results, for the single asset fractional Kelly criterion is derived in the presence of the fat tails associated with subjective uncertainty. For the multi-asset portfolio, Kelly criterion provides an insightful perspective on Risk Parity strategies, which can be extended for the assets with fat tails.

preprint2016arXiv

Statistically validated network of portfolio overlaps and systemic risk

Common asset holding by financial institutions, namely portfolio overlap, is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and thus severe losses at the systemic level. In this paper we propose a method to assess the statistical significance of the overlap between pairs of heterogeneously diversified portfolios, which then allows us to build a validated network of financial institutions where links indicate potential contagion channels due to realized portfolio overlaps. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be in general applied to any bipartite network where the presence of similar sets of neighbors is of interest. We find that the proportion of validated network links (i.e., of statistically significant overlaps) increased steadily before the 2007-2008 global financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that systemic risk from fire sales liquidation was maximal at that time. After a sharp drop in 2008, systemic risk resumed its growth in 2009, with a notable accelerat

preprint2016arXiv

European banking supervision, the role of stress test. Some brief considerations

A quick review of European financial stability institutions and the role of stress tests in the current juridical system.

preprint2016arXiv

Optimal Investment under Information Driven Contagious Distress

We introduce a dynamic optimization framework to analyze optimal portfolio allocations within an information driven contagious distress model. The investor allocates his wealth across several stocks whose growth rates and distress intensities are driven by a hidden Markov chain, and also influenced by the distress state of the economy. We show that the optimal investment strategies depend on the gradient of value functions, recursively linked to each other via the distress states. We establish uniform bounds for the solutions to a sequence of approximation problems, show their convergence to the unique Sobolev solution of the recursive system of Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs), and prove a verification theorem. We provide a numerical study to illustrate the sensitivity of the strategies to contagious distress, stock volatilities and risk aversion.

preprint2010arXiv

Belief Propagation Algorithm for Portfolio Optimization Problems

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. Mézard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

preprint2016arXiv

How to Combine a Billion Alphas

We give an explicit algorithm and source code for computing optimal weights for combining a large number N of alphas. This algorithm does not cost O(N^3) or even O(N^2) operations but is much cheaper, in fact, the number of required operations scales linearly with N. We discuss how in the absence of binary or quasi-binary clustering of alphas, which is not observed in practice, the optimization problem simplifies when N is large. Our algorithm does not require computing principal components or inverting large matrices, nor does it require iterations. The number of risk factors it employs, which typically is limited by the number of historical observations, can be sizably enlarged via using position data for the underlying tradables.

preprint2016arXiv

The hierarchical generalized linear model and the bootstrap estimator of the error of prediction of loss reserves in a non-life insurance company

This paper presents the hierarchical generalized linear model (HGLM) for loss reserving in a non-life insurance company. Because in this case the error of prediction is expressed by a complex analytical formula, the error bootstrap estimator is proposed instead. Moreover, the bootstrap procedure is used to obtain full information about the error by applying quantiles of the absolute prediction error. The full R code is available on the Github https://github.com/woali/BootErrorLossReserveHGLM.

preprint2016arXiv

Generalization of Doob Decomposition Theorem and Risk Assessment in Incomplete Markets

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of equivalent measures. The description of all local regular supermartingales relative to a convex set of equivalent measures is presented. A notion of complete set of equivalent measures is introduced. We prove that every non negative bounded supermartingale relative to a complete set of equivalent measures is local regular. A new definition of fair price of contingent claim in incomplete market is given and a formula for fair price of Standard option of European type is found.

preprint2016arXiv

A Model of Synchronization for Self-Organized Crowding Behavior

This paper proposes a general model for synchronized crowding behavior. An order parameter is introduced to quantify the level of synchronization which is shown a function of percentage of agents in reactive state. Further, synchronization is shown to be driven by the most active agents with the highest volatility. A tipping point is identified when crowd becomes self-amplifying and unstable. By applying this model, financial bubbles, market momentum and volatility patterns are simulated.

preprint2016arXiv

Financial Contagion and Asset Liquidation Strategies

This paper provides a framework for modeling the financial system with multiple illiquid assets during a crisis. This work generalizes the paper by Amini, Filipovic and Minca (2016) by allowing for differing liquidation strategies. The main result is a proof of sufficient conditions for the existence of an equilibrium liquidation strategy with corresponding unique clearing payments and liquidation prices. An algorithm for computing the maximal clearing payments and prices is provided.

preprint2013arXiv

Hedging Against the Interest-rate Risk by Measuring the Yield-curve Movement

By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and the twist. The empirical analysis shows that our hedging strategies are comparable to traditional duration-convexity strategy, or even better when we have more suitable hedging instruments on hand. The article shows that this strategy is flexible and robust to cope with the interest-rate risk and can help fine-tune a position as time changes.

preprint2016arXiv

Crunching Mortality and Life Insurance Portfolios with extended CreditRisk+

Using an extended version of the credit risk model CreditRisk+, we develop a flexible framework with numerous applications amongst which we find stochastic mortality modelling, forecasting of death causes as well as profit and loss modelling of life insurance and annuity portfolios which can be used in (partial) internal models under Solvency II. Yet, there exists a fast and numerically stable algorithm to derive loss distributions exactly, even for large portfolios. We provide various estimation procedures based on publicly available data. Compared to the Lee-Carter model, we have a more flexible framework, get tighter bounds and can directly extract several sources of uncertainty. Straight-forward model validation techniques are available.

preprint2016arXiv

Dynamics of multivariate default system in random environment

We consider a multivariate default system where random environmental information is available. We study the dynamics of the system in a general setting and adopt the point of view of change of probability measures. We also make a link with the density approach in the credit risk modelling. In the particular case where no environmental information is concerned, we pay a special attention to the phenomenon of system weakened by failures as in the classical reliability system.

preprint2014arXiv

Impact of credit default swaps on financial contagion

It had been believed in the conventional practice that the risk of a bank going bankrupt is lessened in a straightforward manner by transferring the risk of loan defaults. But the failure of American International Group in 2008 posed a more complex aspect of financial contagion. This study presents an extension of the asset network systemic risk model (ANWSER) to investigate whether credit default swaps mitigate or intensify the severity of financial contagion. A protection buyer bank transfers the risk of every possible debtor bank default to protection seller banks. The empirical distribution of the number of bank bankruptcies is obtained with the extended model. Systemic capital buffer ratio is calculated from the distribution. The ratio quantifies the effective loss absorbency capability of the entire financial system to force back financial contagion. The key finding is that the leverage ratio is a good estimate of a systemic capital buffer ratio as the backstop of a financial system. The risk transfer from small and medium banks to big banks in an interbank network does not mitigate the severity of financial contagion.

preprint2013arXiv

Optimal portfolio for a robust financial system

This study presents an ANWSER model (asset network systemic risk model) to quantify the risk of financial contagion which manifests itself in a financial crisis. The transmission of financial distress is governed by a heterogeneous bank credit network and an investment portfolio of banks. Bankruptcy reproductive ratio of a financial system is computed as a function of the diversity and risk exposure of an investment portfolio of banks, and the denseness and concentration of a heterogeneous bank credit network. An analytic solution of the bankruptcy reproductive ratio for a small financial system is derived and a numerical solution for a large financial system is obtained. For a large financial system, Large diversity among banks in the investment portfolio makes financial contagion more damaging on the average. But large diversity is essentially effective in eliminating the risk of financial contagion in the worst case of financial crisis scenarios. A bank-unique specialization portfolio is more suitable than a uniform diversification portfolio and a system-wide specialization portfolio in strengthening the robustness of a financial system.

preprint2016arXiv

Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall

Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calculated - can be based on a simultaneous multinomial test of value-at-risk (VaR) exceptions at different levels, an idea supported by an approximation of ES in terms of multiple quantiles of a distribution proposed in Emmer et al. (2015). By comparing Pearson, Nass and likelihood-ratio tests (LRTs) for different numbers of VaR levels $N$ it is shown in a series of simulation experiments that multinomial tests with $N\geq 4$ are much more powerful at detecting misspecifications of trading book loss models than standard binomial exception tests corresponding to the case $N=1$. Each test has its merits: Pearson offers simplicity; Nass is robust in its size properties to the choice of $N$; the LRT is very powerful though slightly over-sized in small samples and more computationally burdensome. A traffic-light system for trading book models based on the multinomial test is pro

preprint2016arXiv

On the aggregation of experts' information in Bonus-Malus systems

We present in this paper a new premium computation principle based on the use of prior information from multiple sources for computing the premium charged to a policyholder. Under this framework, based on the use of Ordered Weighted Averaging (OWA) operators, we propose alternative collective and Bayes premiums and describe some approaches to compute them. Several examples illustrates the new framework for premium computation.

preprint2016arXiv

Density Forecasts and the Leverage Effect: Some Evidence from Observation and Parameter-Driven Volatility Models

The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity returns using well-known observation and parameter-driven volatility models. These models differ in their assumptions regarding: The parametric specification, the evolution of the conditional volatility process and how the leverage effect is accounted for. The ability of a model to generate accurate density forecasts when the leverage effect is incorporated or not as well as a comparison between different model-types is carried out using a large number of financial time-series. We find that, models with the leverage effect generally generate more accurate density forecasts compared to their no-leverage counterparts. Moreover, we also find that our choice with regards to how to model the leverage effect and the conditional log-volatility process is important in generating accurate density forecasts

preprint2014arXiv

A new multivariate dependence measure based on comonotonicity

In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and relations between the new dependence measure and other multivariate measures are an- alyzed. We also give several characteristics of this measure and estimations based on the definitions and its property are presented.

preprint2016arXiv

Intragroup transfers, intragroup diversification and their risk assessment

When assessing group solvency, an important question is to what extent intragroup transfers may be considered, as this determines to which extent diversification can be achieved. We suggest a framework to describe the families of admissible transfers that range from the free movement of capital to excluding any transactions. The constraints on admissible transactions are described as random closed sets. The paper focuses on the corresponding solvency tests that amount to the existence of acceptable selections of the random sets of admissible transactions.

preprint2015arXiv

Multivariate Stop loss Mixed Erlang Reinsurance risk: Aggregation, Capital allocation and Default risk

In this paper, we address the aggregation of dependent stop loss reinsurance risks where the dependence among the ceding insurer(s) risks is governed by the Sarmanov distribution and each individual risk belongs to the class of Erlang mixtures. We investigate the effects of the ceding insurer(s) risk dependencies on the reinsurer risk profile by deriving a closed formula for the distribution function of the aggregated stop loss reinsurance risk. Furthermore, diversification effects from aggregating reinsurance risks are examined by deriving a closed expression for the risk capital needed for the whole portfolio of the reinsurer and also the allocated risk capital for each business unit under the TVaR capital allocation principle. Moreover, given the risk capital that the reinsurer holds, we express the default probability of the reinsurer analytically. In case the reinsurer is in default, we determine analytical expressions for the amount of the aggregate reinsured unpaid losses and the unpaid losses of each reinsured line of business of the ceding insurer(s). These results are illustrated by numerical examples.

206 works