Risk Dynamics Actuarial Traineeship Topics

CONFIDENTIAL

Traineeship Topics

Dr. Céline Azizieh, Associate Partner

Dr. Jérome Barbarin, Expert

Dr. Julien Trufin, Manager

Brussels, March 28th 2012

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2012 2Trainiship Proposals


Traineeship Topics ● Topic 1: Open questions in Non-Life

● Topic 2: Optimization of nested simulations

● Topic 3: Interest rates modelling

Agenda



Open Questions in Non-Life

2012Trainiship Proposals 4


Large claims vs attritional claims ● Investigation of the existing methods for separating the small claims and the large claims,

including techniques derived from the Extreme Value Theory;

Reserving in non-life ● Investigation of the last academics developments (e.g. Mario Wuthrich) + Application on

the Belgian market triangles in order to assess the impact of those methods on real data sets;

Underwriting cycles● The problematic of the underwriting cycles, and their implications in the context of

Solvency II

Why is it of interest for Risk Dynamics?● Knowing the impact of such methodological choices on the capital is important for our

validation

● It would allow us to give our clients better informed advices

Open Questions in Non-Life



Optimization of Nested Simulations



Context: ● The Solvency II regulation requires the computation of the distribution of the market

consistent values of the assets and of the liabilities (the technical provisions) in one year

● This distribution is computed thanks to the simulations of different risk factors (ex: interest rates, mortality rates, ..) on which depend the values of the assets and liabilities

● Unfortunately, in some cases, no closed form solution exists for the value of these assets and liabilities as a function of the simulated risk factors

● One has thus to rely on numerical techniques to estimate these values

This requires the implementation of Nested Monte-Carlo simulations● Simulations into simulations

Least Square Monte Carlo Method

7

t10Real world

projection

Risk neutral

projection

Risk Measures

at 1-year horizon


In practice, this solution is extremely time and memory consuming

Now, Solvency II regulation insists that the company must be able to produce results in a useful timescale

Different alternative techniques have been considered:● Replicating Portfolio

It has become a popular method in practice but it looks like this method does not always give accurate and stable results

It is only useful for market risk capital charge estimation

● Least Square Monte-Carlo (LSM) method

● Curve Fitting

● Scenarios Selection / Reduction



Least Square Monte Carlo:● This method has been originally developed to price American options with MC simulations

● It has been shown that this method can also be used in a Solvency II context

● The value of the assets and liabilities are estimated thanks to least square regressions on some basis functions of the risk factors

● The main advantage of this method is that we work with a single set of simulations No need of simulations into simulations

Instead of working simulation by simulation, this method uses all the simulations simultaneously

Objectives of the traineeship● Practical application of this technique (in Life or (possibly in non-Life))

● To study its accuracy and ability to approximate the full nested simulation scheme

● To study its stability

● To study its computational efficiency

Least Square Monte Carlo Method

9


Curve fitting● This technique consist to use a polynomial function to mimic the behaviour of best

estimate of technical provisions

● Calibration performed by trying to calculate the BE under a set of (stress and base case) scenarios, and to fit the resulting data points by an analytical formula

Transfer Scenario Order● This consist to identifyt of a target subset of scenarios and avoiding running the BE

calculation through unnecessary scenarios

● Scenarios concerned here are the ones leading to the risk metric (real world scenarios)

● Identification from running the full nested simulation on a representative part of insurancepolicies

Representative Scenarios ● This consist to identify a subset of scenarios representative, under some criteria, of the

full set of scenarios

● Different variations of this technique exist (modified Euclidian distance, relative presentvalue distance, significance method, scenario cluster modelling)




Importance sampling● This technique consists to select more scenarios from the parts of the P&L

distribution that are more critical to the current calculation

Why is it of interest for Risk Dynamics?● The constant concern of the validation is to ensure that the client measures its risks

adequately. We must therefore ensure that the methodological/modelling choices relative to the approximation of the SCR are appropriate and do not neither underestimated nor overestimated the capital

Purpose of the traineeship● Review and study these alternative methodologies:

Study their accuracy and ability to approximate the full nested simulation scheme

Study their impact on the risk capital figures for an insurance company based on a real data set or on a study case

● Practical application of these techniques and study of their computational efficiency

● Study their stability from back-testing

● Comparison of the different methodologies

● Investigate the existing calibration methodologies and measure their impact




Interest Rates Modelling



What is the Libor Market Model?● An interest rate model broadly used by banks for pricing interest rates options

● Used by most banks in conjunction with a SABR model

● In this model, the factors are a set of forward rates corresponding to the ones observed in the market on a continuous basis, regularly spaced in time

Why is it important in the Solvency II context?● Interest rates represent a key risk factor in the risk taxonomy of companies

In Life insurance (profit sharing, lapse)

But also in non-life insurance, when cash-flows depend on inflation

● The capital for interest rate risk is generally an important part of the overall capital

● Any company needs to develop an Economic Scenarios Generator In order to calculate their capital within an internal model approach

Even within the standard formula, for calculating the best estimate of liabilities when cash-flows strongly depend in the level of interest rates in the market, in a nonlinear way

● The way interest rates are modelled can have a huge impact on the final capital figures

Libor Market Model

132012Trainiship Proposals


Why is it of interest for Risk Dynamics?● More and more companies use the LMM due to its properties

● This model can be declined in many ways

● The constant concern of the validation is to ensure that the client measures its risks adequately, and also manage its model risk Model risk is present in any modelling exercise, especially at the level of interest rates, and we

need to have a clear view on the possible impact of the different LMM formulations

We must be able to assist the client with a benchmarking of their interest rate model calibration or interest rate risk capital measurement

Purpose of the traineeship● Review the main existing LMM formulations

Study/testing their calibration ease, investigation of the different calibration methodologies, measure of the impact on the final capital on a practical case, analysis of the differences in terms of statistical properties,…

Consistency between risk neutral and real world calibration based on market and historical data (testing of different coherent calibration approaches)

Understanding properties of the different formulations

Libor Market Model

142012Trainiship Proposals

Career

Risk Dynamics Actuarial Traineeship Topics