Extreme Moves in Foreign Exchange Rates and Risk Limit Setting

Foreign exchange rates can be subject to considerable daily fluctuations (up to 5 percent within one day). This can, in certain cases, cause serious losses on open overnight positions. Given a maximum tolerable loss for a company, limits have to be set on open overnight positions in foreign currencies. Usually, these limits are determined by using a normal ("Gaussian") model for the daily fluctuations. In our study we illustrate how this common model sometimes quite strongly underestimates the actual extreme risks and, based on methods from the Extreme Value Theory (EVT), we propose and justify a more accurate model.extreme value theory, risk management, foreign exchange, time series analysis

Estimating the risk-adjusted capital is an affair in the tails

(Re)insurance companies need to model their liabilities' portfolio to compute the risk-adjusted capital (RAC) needed to support their business. The RAC depends on both the distribution and the dependence functions that are applied among the risks in a portfolio. We investigate the impact of those assumptions on an important concept for (re)insurance industries: the diversification gain. Several copulas are considered in order to focus on the role of dependencies. To be consistent with the frameworks of both Solvency II and the Swiss Solvency Test, we deal with two risk measures: the Value-at-Risk and the expected shortfall. We highlight the behavior of different capital allocation principles according to the dependence assumptions and the choice of the risk measure.Capital Allocation, Copula, Dependence, Diversification Gain, Model Uncertainty, Monte Carlo Methods, Risk-Adjusted Capital, Risk Measure

Dynamic Financial Analysis - Understanding Risk and Value Creation in Insurance

The changing business environment in non-life insurance and reinsurance has raised the need for new quantitative methods to analyze the impact of various types of strategic decisions on a company’s bottom line. Dynamic Financial Analysis («DFA») has become popular among practitioners as a means of addressing these new requirements. It is a systematic approach based on large-scale computer simulations for the integrated financial modeling of non-life insurance and reinsurance companies aimed at assessing the risks and the benefits associated with strategic decisions. DFA allows decision makers to understand and quantify the impact and interplay of the various risks that their company is exposed to, and – ultimately – to make better informed strategic decisions. In this brochure, we provide an overview and assessment of the state of the industry related to DFA. We investigate the DFA value proposition, we explain its elements and we explore its potential and limitations.reinsurance, dynamic financial analysis, insurance

The impact of systemic risk on the diversification benefits of a risk portfolio

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is lowComment: 17 pages, 5 tableau

Credit Risk Models - Do They Deliver Their Promises? A Quantitative Assessment

We develop a framework to assess the statistical significance of expected default frequency as calculated by credit risk models. This framework is then used to analyze the quality of two commercially available models that have become popular among practitioners: KMV Credit Monitor and RiskCalc from Moody's. Using a unique database of expected default probability from both vendors, we study both the consistency of predictions and their timeliness. We introduce the concept of cumulative accuracy profile (CAP), which allows to see in one curve the percentage of companies whose defualts were captured by the models one year in advance. We also use the Miller's information test to see if the models add information to the S&P rating. The result of the analysis indicates that these models indeed add relevant information not accounted for by rating alone. Moreover, with respect to rating agencies, the models predict defaults more than ten months in advance on average.credit risk models, cumulative accuracy profile, risk modeling

How Much Reinsurance Do You Really Need? A Case Study.

Today’s reinsurance manager has to balance many diverging interests. Most prominent among these are the risk-return objectives of the company owners and the security requirements of the policyholders. Performance measurement issues and the sheer number of available reinsurance and capital market solutions further complicate the decision-making process. Given the complexity of the problem, it has been our experience that a quantitative approach can help in understanding the risks and the cost of financing them. This leads to more informed decisions. In this article, we guide the reader through the steps of restructuring an existing traditional reinsurance program using quantitative models of the risks. This is done by means of a case study in which concrete insurance lines are analyzed in a sample portfolio.reinsurance, alternative risk transfer, asset liability management, dynamic financial analysis

Risk aggregation, dependence structure and diversification benefit

Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include them in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits. To compute the total risk of a portfolio, it is important to establish the rules for aggregating the various risks that compose it. This can only be done through modelling of their dependence. It is a well known fact among traders in financial markets that "diversification works the worst when one needs it the most''. In other words, in times of crisis the dependence between risks increases. Experience has shown that very large loss events almost always affect multiple lines of business simultaneously. September 11, 2001, is an example of such an event: when the claims originated simultaneously from lines of business which are usually uncorrelated, such as property and life, at the same time that the assets of the company were depreciated due to the crisis on the stock markets. In this paper, we explore various methods of modelling dependence and their influence on diversification benefits. We show that the latter strongly depend on the chosen method and that rank correlation grossly overestimates diversification. This has consequences on the RBC for the whole portfolio, which is smaller than it should be when correctly accounting for tail correlation. However, the problem remains to calibrate the dependence for extreme events, which are rare by definition. We analyze and propose possible ways to get out of this dilemma and come up with reasonable estimates.Risk-Based Capital, Hierarchical Copula, Dependence, Calibration

The price of being a Systemically Important Financial Institution (SIFI)

After reviewing the notion of Systematically Important Financial Institution (SIFI), we propose a first principles way to compute the price of the implicit put option that the State gives to such an institution. Our method is based on important results from Extreme Value Theory (EVT), one for the aggregation of heavy tailed distributions and the other one for the tail behavior of the Value-at-Risk (VaR) versus the Tail-Value-at-Risk (TVaR). We show how to value in practice is proportional to the VaR of the institution and thus would provide the wrong incentive to the banks even if not explicitly granted. We conclude with a proposal to make the institution pay the price of this option to a fund, whose task would be to guarantee the orderly bankruptcy of such an institution. This fund would function like an insurance selling a cover to clients

Bootstrapping the economy -- a non-parametric method of generating consistent future scenarios

The fortune and the risk of a business venture depends on the future course of the economy. There is a strong demand for economic forecasts and scenarios that can be applied to planning and modeling. While there is an ongoing debate on modeling economic scenarios, the bootstrapping (or resampling) approach presented here has several advantages. As a non-parametric method, it directly relies on past market behaviors rather than debatable assumptions on models and parameters. Simultaneous dependencies between economic variables are automatically captured. Some aspects of the bootstrapping method require additional modeling: choice and ransformation of the economic variables, arbitrage-free consistency, heavy tails of distributions, serial dependence, trends and mean reversion. Results of a complete economic scenario generator are presented, tested and discussed.economic scenario generator (ESG); asset-liability management (ALM); bootstrapping; resampling; simulation; Monte-Carlo simulation; non-parametric model; yield curve model

Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Scaling exponents; Time series analysis; Multi-fractals