Value-at-Risk time scaling for long-term risk estimation

In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the usual market-risk measure, ie, Value-at-Risk (VaR) at a short-term horizon and 99% confidence level, by properly applying a scaling on the short-term Profit-and-Loss (P&L) distribution. Besides the standard square-root-of-time scaling, based on normality assumptions, we consider two leptokurtic probability density function classes for fitting empirical P&L datasets and derive accurately their scaling behaviour in light of the Central Limit Theorem, interpreting time scaling as a convolution problem. Our analyses result in a range of possible VaR-scaling approaches depending on the distribution providing the best fit to empirical data, the desired percentile level and the time horizon of the Economic Capital calculation. After assessing the different approaches on a test equity trading portfolio, it emerges that the choice of the VaR-scaling approach can affect substantially the Economic Capital calculation. In particular, the use of a convolution-based approach could lead to significantly larger risk measures (by up to a factor of four) than those calculated using Normal assumptions on the P&L distribution.Comment: Pre-Print version, submitted to The Journal of Risk. 18 pages, 17 figure

Semi-parametric estimation of joint large movements of risky assets

The classical approach to modelling the occurrence of joint large movements of asset returns is to assume multivariate normality for the distribution of asset returns. This implies independence between large returns. However, it is now recognised by both academics and practitioners that large movements of assets returns do not occur independently. This fact encourages the modelling joint large movements of asset returns as non-normal, a non trivial task mainly due to the natural scarcity of such extreme events. This paper shows how to estimate the probability of joint large movements of asset prices using a semi-parametric approach borrowed from extreme value theory (EVT). It helps to understand the contribution of individual assets to large portfolio losses in terms of joint large movements. The advantages of this approach are that it does not require the assumption of a specific parametric form for the dependence structure of the joint large movements, avoiding the model misspecification; it addresses specifically the scarcity of data which is a problem for the reliable fitting of fully parametric models; and it is applicable to portfolios of many assets: there is no dimension explosion. The paper includes an empirical analysis of international equity data showing how to implement semi-parametric EVT modelling and how to exploit its strengths to help understand the probability of joint large movements. We estimate the probability of joint large losses in a portfolio composed of the FTSE 100, Nikkei 250 and S&P 500 indices. Each of the index returns is found to be heavy tailed. The S&P 500 index has a much stronger effect on large portfolio losses than the FTSE 100, although having similar univariate tail heaviness

Analysis of operational risk of banks – catastrophe modelling

Nowadays financial institutions due to regulation and internal motivations care more intensively on their risks. Besides previously dominating market and credit risk new trend is to handle operational risk systematically. Operational risk is the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. First we show the basic features of operational risk and its modelling and regulatory approaches, and after we will analyse operational risk in an own developed simulation model framework. Our approach is based on the analysis of latent risk process instead of manifest risk process, which widely popular in risk literature. In our model the latent risk process is a stochastic risk process, so called Ornstein- Uhlenbeck process, which is a mean reversion process. In the model framework we define catastrophe as breach of a critical barrier by the process. We analyse the distributions of catastrophe frequency, severity and first time to hit, not only for single process, but for dual process as well. Based on our first results we could not falsify the Poisson feature of frequency, and long tail feature of severity. Distribution of “first time to hit” requires more sophisticated analysis. At the end of paper we examine advantages of simulation based forecasting, and finally we concluding with the possible, further research directions to be done in the future

Resilient livelihoods and food security in coastal aquatic agricultural systems: Investing in transformational change

Aquatic agricultural systems (AAS) are diverse production and livelihood systems where families cultivate a range of crops, raise livestock, farm or catch fish, gather fruits and other tree crops, and harness natural resources such as timber, reeds, and wildlife. Aquatic agricultural systems occur along freshwater floodplains, coastal deltas, and inshore marine waters, and are characterized by dependence on seasonal changes in productivity, driven by seasonal variation in rainfall, river flow, and/or coastal and marine processes. Despite this natural productivity, the farming, fishing, and herding communities who live in these systems are among the poorest and most vulnerable in their countries and regions. This report provides an overview of the scale and scope of development challenges in coastal aquatic agricultural systems, their significance for poor and vulnerable communities, and the opportunities for partnership and investment that support efforts of these communities to secure resilient livelihoods in the face of multiple risks