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At least 91 records · Page 5Linked to original sources
arXiv2009

A duality approach to the worst case value at risk for a sum of dependent random variables with known covariances

We propose an approach to the aggregation of risks which is based on estimation of simple quantities (such as covariances) associated to a vector of dependent random variables, and which avoids the use of parametric families of copulae. Our main result demonstrates that the method leads to bounds on the worst case Value at Risk for a sum of dependent random variables. Its proof applies duality theory for infinite dimensional linear programs.

q-fin.RM↗
arXiv2009

Tails of correlation mixtures of elliptical copulas

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is generally larger than in the limit, which can have serious consequences for estimation and evaluation of extreme risk. Finally, although correlation mixtures of Gaussian copulas inherit the property of asymptotic independence, at the same time they fall in the newly defined category of near asymptotic dependence. The consequences of these findings for modeling are assessed by means of a simulation study and a case study involving financial time series.

math.ST↗
arXiv2009

Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Risk

In this paper we develop structural first passage models (AT1P and SBTV) with time-varying volatility and characterized by high tractability, moving from the original work of Brigo and Tarenghi (2004, 2005) [19] [20] and Brigo and Morini (2006)[15]. The models can be calibrated exactly to credit spreads using efficient closed-form formulas for default probabilities. Default events are caused by the value of the firm assets hitting a safety threshold, which depends on the financial situation of the company and on market conditions. In AT1P this default barrier is deterministic. Instead SBTV assumes two possible scenarios for the initial level of the default barrier, for taking into account uncertainty on balance sheet information. While in [19] and [15] the models are analyzed across Parmalat's history, here we apply the models to exact calibration of Lehman Credit Default Swap (CDS) data during the months preceding default, as the crisis unfolds. The results we obtain with AT1P and SBTV have reasonable economic interpretation, and are particularly realistic when SBTV is considered. The pricing of counterparty risk in an Equity Return Swap is a convenient application we consider, also to illustrate the interaction of our credit models with equity models in hybrid products context.

q-fin.PR↗
arXiv2009

Defining, Estimating and Using Credit Term Structures. Part 2: Consistent Risk Measures

In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are consistent with the survival-based valuation framework. We then show how to use these risk measures for the construction of market neutral portfolios.

q-fin.PR↗
arXiv2009

Dynamic Estimation of Credit Rating Transition Probabilities

We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential time weighting with varying horizons and discuss the underlying dynamics of transition generator matrices in the long-term and short-term estimation horizons.

q-fin.ST↗
arXiv2010

The Underlying Dynamics of Credit Correlations

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches.

q-fin.PR↗
arXiv2010

Allocation d'actifs selon le critère de maximisation des fonds propres économiques en assurance non-vie

The economic equities maximization criterion (MFPE) leads to the choice of financial portfolio, which maximizes the ratio of the expected value of the insurance company on the capital. This criterion is presented in the framework of a non-life insurance company and is applied within the framework of the French legislation and in a lawful context inspired of the works in progress about the European project Solvency 2. In the French regulation case, the required solvency margin does not depend of the asset allocation. It is quite different in the Solvency 2 framework because the target capital has to control the global risk of the company. And the financial risk takes part of this global risk. Thus the economic equities maximization criterion leads to search a couple asset allocation / equities which solves a stochastic program. A numerical illustration makes it possible to analyze the consequences of the introduction of a Solvency 2 framework on the technical reserves and the equities of a non-life insurance company and on the optimal allocation due to the economic equities maximization criterion. Finally, the impact of a misspecification of the risky asset model on the optimal allocation is illustrated.

q-fin.RM↗
arXiv2010

Mesure des risques de marché et de souscription vie en situation d'information incomplète pour un portefeuille de prévoyance

In the framework of Embedded Value new standards, namely the MCEV norms, the latest principles published in June 2008 address the issue of market and underwriting risks measurement by using stochastic models of projection and valorization. Knowing that stochastic models particularly data-consuming, the question which can arise is the treatment of insurance portfolios only available in aggregate data or portfolios in situation of incomplete information. The aim of this article is to propose a pragmatic modeling of these risks tied up with death covers of individual protection products in these situations.

q-fin.RM↗
arXiv2010

Mesure de l'incertitude tendancielle sur la mortalité ? application à un régime de rentes

The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic prospective tables thus built make it possible to project the evolution of the random mortality rates in the future and to quantify the systematic risk of mortality.

q-fin.GN↗
arXiv2010

Etude du risque systématique de mortalité

The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic prospective tables thus built make it possible to project the evolution of the random mortality rates in the future and to quantify the systematic risk of mortality.

q-fin.GN↗
arXiv2010

Dual Representation of Quasiconvex Conditional Maps

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

q-fin.RM↗
arXiv2010

Optimal Reversible Annuities to Minimize the Probability of Lifetime Ruin

We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; or (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexiblity to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual's annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.

q-fin.RM↗
arXiv2010

Hidden Regular Variation: Detection and Estimation

Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{E} = [0, \infty]^d \backslash \{(0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{E}^{(2)} = \mathbb{E} \backslash \cup_{i=1}^d \mathbb{L}_i$, where $\mathbb{L}_i$ is the $i$-th axis. We extend the concept of hidden regular variation to sub-cones of $\mathbb{E}^{(2)}$ as well. We suggest a procedure for detecting the presence of hidden regular variation, and if it exists, propose a method of estimating the limit measure exploiting its semi-parametric structure. We exhibit examples where hidden regular variation yields better estimates of probabilities of risk sets.

math.PR↗
arXiv2010

The Hazards of Propping Up: Bubbles and Chaos

In the current environment of financial distress, many governments are likely to soon become major holders of financial assets, but the policy debate focuses only on the likelihood and extent of short-term market stabilization. This paper shows that government intervention and propping up are likely to lead to long-term bubbles and even wildly chaotic behavior. The discontinuities occur when the committed capital reaches a critical amount that depends on just two parameters: the market impact of trading and the target exposure percentage.

q-fin.GN↗
arXiv2010

Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions

We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit form, which can be compared and interpreted. This paper continues our previous work, where we solved similar problems for power utility functions.

q-fin.PM↗
arXiv2010

Spin Glass Model of Operational Risk

We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We unveil the presence of limit cycles and scrutinize the features of the asymptotic state.

q-fin.RM↗
arXiv2010

Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalized probability measures on the optional sigma-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for different notions of time consistency. In particular we show how bubbles may appear in the dynamic penalization, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.

q-fin.RM↗