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Funded Bilateral Valuation Adjustment

We show how the cost of funding the collateral in a particular set up can be equal to the Bilateral Valuation Adjustment with the "funded" probability of default, leading to the definition of a Funded Bilateral Valuation Adjustment (FBVA). That set up can also be viewed by an investor as an effective way to restructure the counterparty risk arising from an uncollateralized transaction with a counterparty, mitigating or even avoiding entirely the additional capital charge introduced by the new Basel III framework.

q-fin.PR↗

On the new central bank strategy toward monetary and financial instabilities management in finances: Econophysical analysis of nonlinear dynamical financial systems

We describe the innovations in finances, introduced over the recent decades, and analyze most of the business and regulatory challenges, faced by the financial industry, because of the present disruptive changes in the global capital markets. We use the integrative thinking approach to formulate the new central bank strategy and propose that the new strategy has to be focused on the constant management of the monetary and financial instabilities, using the knowledge base in the field of econophysics. We propose the new theoretical model of economics, which is called the Nonlinear Dynamic Stochastic General Equilibrium (NDSGE), which takes to the account the nonlinearities, appearing during the interaction between the business cycles. We show that the central banks, which will apply the knowledge gained from the econophysical analysis to understand the complex processes in the national financial systems in the time of high volatility in global capital markets, will be able to govern the national financial systems successfully.

q-fin.GN↗

On the Risk Management with Application of Econophysics Analysis in Central Banks and Financial Institutions

The purpose of this research article is to discover how the econophysics analysis can complement the econometrics models in application to the risk management in the central banks and financial institutions, operating within the nonlinear dynamical financial system. We consider the modern risk management models and show the appropriate techniques to calculate the various existing risks in the finances. We make a few comments on the possible limitations in the models of statistical modeling of volatility such as the Autoregressive Conditional Heteroskedasticity (GARCH) model, because of the nonlinearities appearance in the nonlinear dynamical financial systems. We propose that the various types of nonlinearities, which can originate in the financial and economical systems, have to be taken to the detailed consideration during the Cost of Capital calculation in the finances and economics. We propose the new theory of nonlinear dynamic volatilities and the new nonlinear dynamic chaos (NDC) volatility model for the statistical modeling of financial volatility with the aim to determine the Value at Risk.

q-fin.GN↗

Closed form solutions of measures of systemic risk

This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier and Acharya et al. have suggested as measures of systemic risk to be attached to individual banks. The statistics equal the product of statistic specific Beta-coefficients with the mean corrected Value at Risk. Hence, the measures of systemic risks are closely related to well known concepts of financial economics. Another benefit of the analysis is that it is revealed how the concepts are related to each other. Also, it may be relatively easy to convince the regulators to consider a closed form solution, especially so if the statistics involved are well known and can easily be communicated to the financial community.

q-fin.RM↗

The Calculus of Expected Loss: Backtesting Parameter-Based Expected Loss in a Basel II Framework

The dependency structure of credit risk parameters is a key driver for capital consumption and receives regulatory and scientific attention. The impact of parameter imperfections on the quality of expected loss (EL) in the sense of a fair, unbiased estimate of risk expenses however is barely covered. So far there are no established backtesting procedures for EL, quantifying its impact with regards to pricing or risk adjusted profitability measures. In this paper, a practically oriented, top-down approach to assess the quality of EL by backtesting with a properly defined risk measure is introduced. In a first step, the concept of risk expenses (Cost of Risk) has to be extended beyond the classical provisioning view, towards a more adequate capital consumption approach (Impact of Risk, IoR). On this basis, the difference between parameter-based EL and actually reported Impact of Risk is decomposed into its key components. The proposed method will deepen the understanding of practical properties of EL, reconciles the EL with a clearly defined and observable risk measure and provides a link between upcoming IFRS 9 accounting standards for loan loss provisioning with IRBA regulatory capital requirements. The method is robust irrespective whether parameters are simple, expert based values or highly predictive and perfectly calibrated IRBA compliant methods, as long as parameters and default identification procedures are stable.

q-fin.RM↗

Optimal portfolio model based on WVAR

This article is focused on using a new measurement of risk-- Weighted Value at Risk to develop a new method of constructing initiate from the TVAR solving problem, based on MATLAB software, using the historical simulation method (avoiding income distribution will be assumed to be normal), the results of previous studies also based on, study the U.S. Nasdaq composite index, combining the Simpson formula for the solution of TVAR and its deeply study; then, through the representation of WVAR formula discussed and indispensable analysis, also using the Simpson formula and the numerical calculations, we have done the empirical analysis and review test. this paper is based on WVAR which possesses better properties, taking the idea of portfolio into the multi-index comprehensive evaluation, to build innovative WVAR based portfolio selection under the framework of a theoretical model; in this framework, a description of risks is designed by WVAR, its advantage is no influence by income distribution, meanwhile various optimization problems have a unique solution; then take AHP weights to different indicators deal on this basis, after that we put a nonlinear satisfaction portfolio selected model forward and conduct tests of empirical analysis, finally we use weighted linear approach to convert the portfolio model into a single-objective problem, which is easier to solve, then we use the data of two ETFs to construct portfolio, and compare the performance of portfolio constructed by Mean-Weighted V@R and by Mean-Variance.

q-fin.RM↗

Parameter estimation of a Levy copula of a discretely observed bivariate compound Poisson process with an application to operational risk modelling

A method is developed to estimate the parameters of a Levy copula of a discretely observed bivariate compound Poisson process without knowledge of common shocks. The method is tested in a small sample simulation study. Also, the method is applied to a real data set and a goodness of fit test is developed. With the methodology of this work, the Levy copula becomes a realistic tool of the advanced measurement approach of operational risk.

q-fin.RM↗

The Illusion of the Perpetual Money Machine

We argue that the present crisis and stalling economy continuing since 2007 are rooted in the delusionary belief in policies based on a "perpetual money machine" type of thinking. We document strong evidence that, since the early 1980s, consumption has been increasingly funded by smaller savings, booming financial profits, wealth extracted from house price appreciation and explosive debt. This is in stark contrast with the productivity-fueled growth that was seen in the 1950s and 1960s. This transition, starting in the early 1980s, was further supported by a climate of deregulation and a massive growth in financial derivatives designed to spread and diversify the risks globally. The result has been a succession of bubbles and crashes, including the worldwide stock market bubble and great crash of October 1987, the savings and loans crisis of the 1980s, the burst in 1991 of the enormous Japanese real estate and stock market bubbles, the emerging markets bubbles and crashes in 1994 and 1997, the LTCM crisis of 1998, the dotcom bubble bursting in 2000, the recent house price bubbles, the financialization bubble via special investment vehicles, the stock market bubble, the commodity and oil bubbles and the debt bubbles, all developing jointly and feeding on each other. Rather than still hoping that real wealth will come out of money creation, we need fundamentally new ways of thinking. In uncertain times, it is essential, more than ever, to think in scenarios: what can happen in the future, and, what would be the effect on your wealth and capital? How can you protect against adverse scenarios? We thus end by examining the question "what can we do?" from the macro level, discussing the fundamental issue of incentives and of constructing and predicting scenarios as well as developing investment insights.

q-fin.GN↗

The art of probability-of-default curve calibration

PD curve calibration refers to the transformation of a set of rating grade level probabilities of default (PDs) to another average PD level that is determined by a change of the underlying portfolio-wide PD. This paper presents a framework that allows to explore a variety of calibration approaches and the conditions under which they are fit for purpose. We test the approaches discussed by applying them to publicly available datasets of agency rating and default statistics that can be considered typical for the scope of application of the approaches. We show that the popular 'scaled PDs' approach is theoretically questionable and identify an alternative calibration approach ('scaled likelihood ratio') that is both theoretically sound and performs better on the test datasets. Keywords: Probability of default, calibration, likelihood ratio, Bayes' formula, rating profile, binary classification.

q-fin.RM↗

Dynamic quasi-concave performance measures

We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characterization of a CPM in terms of an induced family of conditional convex risk measures. In the case of indexes these risk measures are coherent. Then, Dynamic Performance Measures (DPMs) are introduced and the problem of time consistency is addressed. The definition of time consistency chosen here ensures that the positions which are considered good tomorrow are already considered good today. We prove the equivalence between time consistency for a DPM and weak acceptance consistency for the induced families of risk measures. Finally, we extend CPMs and DPMs to dividend processes.

q-fin.PM↗

Risk Measures in a Regime Switching Model Capturing Stylized Facts

We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk measures by Fourier methods that have successfully been applied to option pricing and analyze the accuracy of the results.

q-fin.RM↗

A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very competitive method for the calculation of CV@R which is comparable in computational time to the calculation of V@R. We also develop methods for the efficient computation of risk contributions.

q-fin.RM↗

On Reduced Form Intensity-based Model with Trigger Events

Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts of both observable "trigger" events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. Both single-default and multiple-default cases are considered in this paper. In the former case, a simple expression for the distribution of the default time is obtained. Applications of the proposed model to price defaultable bonds and multi-name Credit Default Swaps (CDSs) are provided.

q-fin.CP↗

On Infectious Model for Dependent Defaults

In this paper, we propose a two-sector Markovian infectious model, which is an extension of Greenwood's model. The central idea of this model is that the causality of defaults of two sectors is in both direction, which enrich dependence dynamics. The Bayesian Information Criterion is adopted to compare the proposed model with the two-sector model in credit literature using the real data. We find that the newly proposed model is statistically better than the model in past literature. We also introduce two measures: CRES and CRVaR to give risk evaluation of our model.

q-fin.RM↗

The Foster-Hart Measure of Riskiness for General Gambles

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst--case risk measure, i.e. the maximal possible loss incurred by that gamble. We also extend the Foster--Hart risk measure to dynamic environments for general distributions and probability spaces, and we show that the extended measure avoids bankruptcy in infinitely repeated gambles.

q-fin.RM↗

Multivariate risk measures: a constructive approach based on selections

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk measure and so consider risk measures of set-valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set-valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. We suggest a definition of the risk measure based on calling a set-valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained selection risk measure is coherent (or convex), law invariant and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set-valued risk measures considered by Kulikov (2008), Hamel and Heyde (2010), and Hamel, Heyde and Rudloff (2013).

q-fin.RM↗

On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation

In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk-measures, which are obtained by iterating a given spectral risk-measure (such as Expected Shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk-measures driven by lattice-random walks, under suitable scaling and vanishing time- and spatial-mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.

math.PR↗

Portfolio Management Approach in Trade Credit Decision Making

The basic financial purpose of an enterprise is maximization of its value. Trade credit management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature assume book profit maximization as the basic financial purpose. These book profitbased models could be lacking in what relates to another aim (i.e., maximization of enterprise value). The enterprise value maximization strategy is executed with a focus on risk and uncertainty. This article presents the consequences that can result from operating risk that is related to purchasers using payment postponement for goods and/or services. The present article offers a method that uses portfolio management theory to determine the level of accounts receivable in a firm. An increase in the level of accounts receivables in a firm increases both net working capital and the costs of holding and managing accounts receivables. Both of these decrease the value of the firm, but a liberal policy in accounts receivable coupled with the portfolio management approach could increase the value. Efforts to assign ways to manage these risks were also undertaken; among them, special attention was paid to adapting assumptions from portfolio theory as well as gauging the potential effect on the firm value.

q-fin.PM↗