St. Petersburg Spring School in Risk Management, Insurance, and Finance 2012

This was the very first School in Risk Management, Insurance, and Finance that started a tradition of spring schools of such a type in St. Petersburg. The First School was organised thanks to a generous donation by Barclays Bank. The lectures were held in the European University's Conference Hall and took place on April 2–4, 2012. They were given by Jan Dhaene (Katholieke Universiteit Leuven, Belgium), Emiliano Valdez (University of Connecticut, USA), and Tim Verdonck (Katholieke Universiteit Leuven, Belgium). The topics included «Superhedging Strategies for Index Options and Measuring Systemic Risk in Stock Markets», «Principles and Methods of Capital Allocation for Enterprise Risk Management», and «The Chain-Ladder Method: Influence Analysis, Robustification and Diagnostic Tool».


The Programme


April 2nd, 2012: Finance day (6 hours)


Superhedging Strategies for Index Options and Measuring Systemic Risk in Stock Markets


Professor Jan Dhaene, Katholieke Universiteit Leuven, Belgium


Summary of the Course

We investigate static super-replicating strategies for European-type call options written on a stock index, that is a weighted sum of stock prices. Both the infinite market case (where prices of the plain vanilla options are available for all strikes) and the finite market case (where only a finite number of plain vanilla option prices are observed) are considered. We show how to construct a portfolio consisting of the plain vanilla options on the different stocks, whose pay-off super-replicates the pay-off of the index option. As a consequence, the price of the super-replicating portfolio is an upper bound for the price of the index option. The super-hedging strategy is model-free in the sense that it is expressed in terms of the observed option prices on the individual stocks. In a second part of the course, we introduce an easy to calculate measure for systemic risk in stock markets. This measure is baptized the Herd Behavior Index (HIX). It is model-independent and forward looking, based on observed option data. In order to determine the degree of systemic risk or herd behavior in a stock market one should compare the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The Herd Behavior Index (HIX) is defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance of this extreme market situation. The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days implied Herd Behavior Index for the Dow Jones Industrial Average.


April 3rd, 2012: Risk Management day (6 hours)}


Principles and Methods of Capital Allocation for Enterprise Risk Management


Professor Emiliano Valdez, University of Connecticut, USA


Summary of the Course

There is a growing need and interest among financial institutions not only to determine the total company capital requirement, but also to allocate this total capital across various business units or product lines. The term "capital allocation" has been used to refer to a fair and equitable sub-division of this total capital requirement; it is indeed similar in concept to a fair division of capital in a diversified portfolio of investments. In this talk, we will examine the principles behind capital allocation for enterprise risk management: what is considered fair and equitable, what are the regulatory requirements, and what methods can be used. Along these principles, we examine a unifying framework for allocating the aggregate capital of a financial firm to its various business units or product lines. This unifying ap-proach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capital be minimized. In essence, this leads us to some degree of fairness and equity because this requires capital to be close to the risk that necessitates holding it. Additionally, this approach is very flexible in the sense that different forms of the objective function can reflect alternative definitions of company risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions. Several examples will be discussed to illustrate and to understand the implications of the results arising from these various methods.


April 4th, 2012: Insurance day (6 hours)}


The chain-ladder method: influence analysis, robustification and diagnostic tool


Tim Verdonck, Katholieke Universiteit Leuven, Belgium


Summary of the Course

The chain-ladder method is a widely used technique to forecast the reserves that have to be kept regarding claims that are known to exist, but for which the actual size is unknown at the time the reserves have to be set. Such claims are often represented in a run-off triangle and hence the goal of claims reserving is to obtain predictions for the lower part of the triangle. Several traditional actuarial methods to complete a run-off triangle, such as the chain-ladder method, can be described by one Generalized Linear Model (GLM). In practice it can be easily seen that even one outlier can lead to a huge over- or un-derestimation of the overall reserve when using the chain-ladder method. This indicates that individual claims can be very influential when determining the chain-ladder estimates. The effect of contamination can be mathematically analyzed by calculating influence functions in the GLM framework corresponding to the chain-ladder method. It is proven that the influence functions are unbounded, confirming the sensitivity of the chain-ladder method to outliers. Robust alternatives are introduced to estimate the future claims reserves in a more outlier resistant way. Based on the influence functions and the robust estimators, a diagnostic tool is presented highlighting the influence of every individual claim on the classical chain-ladder estimates. With this tool it is possible to detect immediately which claims have an abnormally positive or negative influence on the reserve estimates. The robust methodology and the diagnostic tool will be illustrated on some artificial and real data sets.


The Organising Committee

Partners and Supporters

The School greatly benefited from generous donations from



Photo Report of the School 2012