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August 29-30, 2011

 

Workshop on

“Actuarial and Financial Statistics”

Satellite
to 58th World Statistics Congress of the
International Statistical Institute 

     (link to ISI)

SUMMARY REGISTRATION SPEAKERS

PROGRAMME

ABSTRACTS


Summary

The International Statistical Institute (ISI) World Statistics Congress, recurring every two years and being among the main activities of the ISI, takes place in Dublin, Ireland, on 21-26 August, 2011. Following the 2011 ISI World Statistics Congress, EURANDOM organizes a EURANDOM-ISI Satellite Workshop. This workshop will be concerned with statistics, focusing on insurance and financial applications.

Topics to be covered include, but are not limited to:

a. Statistics of LÚvy processes in insurance and finance
b. Mortality statistics
c. Statistics of the term structure of interest rates
d. Extreme value statistics

Recent developments in financial markets and financial institutions, such as banks, insurance companies and pension funds, have made explicit that the commonly used models, techniques and tools feature severe shortcomings. There are a number of potential reasons for this state-of-the-art. They include:

1. The high dimensionality of the problems under consideration often forces analysts to rely on Monte Carlo simulation methods of which the reliability is not always guaranteed, in particular not in a risk management setting.

2. The adopted models are often too simplistic, and do, for example, not quickly incorporate the arrival of market information, nor do they incorporate sophisticated dependence structures between the risks. Furthermore, the effect of model risk is often not taken into account.

3.The risk measures under consideration are often specified in terms of high quantiles the estimation of which may rely on extreme value theory. But a treatment which is based on extreme value theory may perform at its own extremes when the central part of the data is entirely ignored, or when second order properties are not taken into account.

4. Economic modeling in many cases suffers from the non-observability of the basic ingredients and results are in many cases highly sensitive to the adopted filtering, instrumental variables, or substitution approach. This is true for example in interest rate modeling.

5. While LÚvy processes have been generally accepted to provide useful models, their statistical treatment is still in its infancy, especially in a high-dimensional setting.

 

Organisers

Prof. Jef Teugels Catholic University Leuven and EURANDOM, President of the ISI (jef.teugels"at"wis.kuleuven.ac.be)
Prof. Roger Laeven Tilburg University and EURANDOM (r.j.a.laeven"at"uvt.nl)
Prof. Wim Schoutens Catholic University Leuven and EURANDOM (wim.schoutens"at"wis.kuleuven.be)

 

 

Registration (is closed)

Registration is obligatory for all participants (organizers and speakers too!).

Registration fee is 75 euros, to be paid by all participants (excluding organizers and speakers).
TU/e personnel only pay 35 euro if they want to join the conference dinner.

 

 

 

Invited speakers

45 min talks by:  
Emiliano Valdez University of Connecticut
MichŔle Vanmaele University of Ghent
Kees Oosterlee CWI
Roger Laeven University of Tilburg
Chris Klaassen University of Amsterdam
   
30 min talks by:  
Dacheng Xiu University of Chicago, Booth School of Business
S.Umut Can EURANDOM and University of Tilburg
Andrea Krajina University of G÷ttingen
Mitja Stadje University of Tilburg
Florence Guillaume EURANDOM
Tim Verdonck Catholic University Leuven
Sara Maccaferri JRC-ISPRA
Katrien Antonio University of Amsterdam

 


Programme

Monday August 29

09.30 - 09.55 Registration  
09.55 - 10.00 Opening Remco van der Hofstad (Scientific Director Eurandom)
10.00 - 10.45 Emiliano Valdez Longitudinal Modeling of Insurance Claim Counts
10.45 - 11.30 Chris Klaassen Semiparametric Estimation Theory for Discretely Observed LÚvy Processes
11.30 - 12.00 Coffee/tea break  
12.00 - 12.45 Cees Oosterlee Efficient Valuation Methods for Contracts in Finance and Insurance
12.45 - 14.00 Lunch  
14.00 - 14.30 Katrien Antonio Micro-level Stochastic Loss Reserving for General Insurance
14.30 - 15.00 Umut Can Goodness of Fit Testing with Empirical Copulas
15.00 - 15.15 Coffee/tea break  
15.15 - 15.45 Andrea Krajina Modeling Jump Dependence using LÚvy Copulas
15.45 - 16.15 Florence Guillaume Multivariate Asset Pricing Models: Some Extensions of the αVG Model
18.00 - Conference dinner  

There will be a poster presentation during the breaks

Tuesday August 30

10.00 - 10.45 MichŔle Vanmaele F÷llmer-Schweizer or Galtchouck-Kunita-Watanabe Decomposition? A Comparison and Description
10.45 - 11.30 Roger Laeven Model Uncertainty and Robustness: A Dual Theory for Decision under Risk and Ambiguity
11.30 - 12.00 Coffee/tea break  
12.00 - 12.30 Dacheng Xiu Dissecting and Deciphering European Option Prices using Closed-Form Series Expansion
12.30 - 14.00 Lunch  
14.00 - 14.30 Sara Maccaferri LÚvy Processes and the Financial Crisis: can we design a more effective Deposit Protection?
14.30 - 15.00 Tim Verdonck Robust Covariance Estimation for Financial Applications
15.00 - 15.15 Coffee/tea break  
15.15 - 15.45 Mitja Stadje Robust Portfolio Choice

 


Abstracts

Katrien Antonio (University of Amsterdam)

Micro-level stochastic loss reserving for general insurance
(joint work with Richard Plat)

To meet future liabilities general insurance companies will set–up reserves. Predicting future cash–flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature  about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run–off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as ‘micro–level data’. We investigate whether the use of such micro–level claim data can improve the reserving process. A realistic micro–level data set on liability claims (material and injury) froma European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an out–of–sample prediction exercise we show that the micro–level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case–study reserve calculations based on the micro–level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way.

PRESENTATION


Umut Can (EURANDOM and University of Tilburg)

Goodness of Fit Testing with Empirical Copulas
(joint work with J. Einmahl, R. Laeven)

Copulas are increasingly used in finance and actuarial sciences to model multivariate dependence. A fundamental question in this respect is the goodness-of-fit of a specified parametric family of copulas for a given sample of multivariate observations. We propose a sequential scanning innovation operation to transform the empirical copula process asymptotically into a standard Wiener process. This transformation paves the way to the development of a variety of asymptotically distribution-free goodness-of-fit tests for copula-based models.

PRESENTATION


Florence Guillaume (Eurandom)

Multivariate Asset Pricing Models: Some Extensions of the αVG Model

We propose a class of multivariate LÚvy and Sato models for option pricing built upon a LÚvy or Sato time change Brownian motion where the time change consists of a weighted sum of an idiosyncratic and a common component. We consider the particular case of Gamma subordinators and we distinguish in between a reduced model where the asset logreturn margins are of Variance Gamma (VG) type and a generalized model where the margins remain LÚvy or Sato-distributed but not necessarily VG distributed anymore. These models can be seen as an extension of the αVG model proposed by Semeraro [1] where the VG margins are replaced by more flexible distributions. We calibrate the different models for a period ranging from June 2008 until October 2009 including therefore the recent credit crisis period. In particular, we show that the reduced models usually fail to reproduce the market correlations when calibrated by using the decoupling calibration procedure whereas the generalized models can adequately reproduce the market implied correlations when a penalty term which assesses the correlation goodness of fit is included into the calibration surface optimizer. Moreover, the proposed Sato models are able to fit univariate option surfaces quotes both for low and high volatility regime periods and consequently outperform both the multivariate Black-Scholes model and the proposed multivariate LÚvy models.

[1] Semeraro, P. (2008). A multivariate Variance Gamma model for financial applications. International Journal of Theoretical and Applied Finance, 11, 1-18.

PRESENTATION


Chris Klaassen (University of Amsterdam)

Semiparametric Estimation Theory for Discretely Observed L'evy Processes
(joined work with Enno Veerman)

For discretely observed LÚvy processes we have to deal with data with an infinitely divisible distribution. We show that for every such distribution the corresponding location family is complete. As a consequence it can be proved that the semiparametric statistical model for our data is nonparametric, in fact.
This has important consequences for efficient inference based on discretely observed LÚvy processes.

PRESENTATION


Andrea Krajina (University of G÷ttingen)

Modeling Jump Dependence using LÚvy Copulas
(Joint work with Roger Laeven)

Abstract

PRESENTATION


Roger Laeven (University of Tilburg)

Model Uncertainty and Robustness: A Dual Theory for Decision under Risk and Ambiguity

This paper axiomatizes a new theory for decision under risk and ambiguity. Our theory is dual to the theory of variational preferences, introduced by Maccheroni, Marinacci and Rustichini (2006). As a special case, we obtain a preference axiomatization of a decision theory that is dual to the popular maxmin expected utility theory of Gilboa and Schmeidler (1989). In addition, we discuss the possibility of resolving paradoxes that appear in other decision theories and characterize risk and ambiguity aversion within our new theory.
(based on joint work with Mitja A. Stadje)

PRESENTATION


Sara Maccaferri (KU Leuven)
(joint work with J. Cariboni, W. Schoutens)

LÚvy processes and the financial crisis: can we design a more effective deposit protection?

LÚvy processes have been applied in various financial settings to overcome the main shortcomings of the Gaussian distribution, since they allow for fat tails and jumps. In the present paper we propose to use LÚvy processes to simulate the distribution of losses deriving from bank failures. The application of LÚvy processes is expected to provide successful results to this aim since bank failures are unexpected, rare events.
We propose to use the simulated distribution of losses to design an effective Deposit Guarantee Schemes (DGSs). DGSs are financial institutions whose main aim is to provide a safety net for depositors. If a credit institution fails, depositors will be able to recover their bank deposits up to a certain limit. During the recent global financial crisis, DGSs were brought at the centre of the political and financial debate, especially due to the fact that the DGSs in the European Union Member States resulted in most of the cases incapable to react to the financial crisis, especially due to the lack of funds set aside. By simulating banks' default and the corresponding losses, our model allows defining a target level for the funds to be collected be the scheme in order to promptly and effectively respond to financial crisis and protect the citizens. The proposed approach is applied to a sample of Italian banks.

PRESENTATION


Kees Oosterlee (CWI)

Efficient valuation methods for contracts in finance and insurance

In this presentation we will discuss the use of Fourier cosine expansions for pricing financial and insurance derivative contracts.
We will discuss hybrid SDE models, like the Heston Hull-White model, modelling for example inflation options, and stochastic control problems.

PRESENTATION


Mitja Stadje

Robust Portfolio Choice

 


Michele Vanmaele (University of Ghent)

F÷llmer-Schweizer or Galtchouck-Kunita-Watanabe decomposition? A comparison and description.

The relationship between the F÷llmer-Schweizer (FS) decomposition and the Galtchouk–Kunita–Watanabe decomposition will be elaborated under the minimal martingale measure. The difference between these two decompositions is highlighted in a very practical example, and the martingale tools that enhance this difference are illustrated in the semimartingale framework as well. The FS-decomposition will be described using the predictable characteristics.

PRESENTATION


Emiliano Valdez (University of Connecticut)
(joint work with Peng Shi, Northern Illinois University)

Longitudinal Modeling of Insurance Claim Counts

Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article considers using copulas to model the number of insurance claims in a longitudinal context. To address the limitations of copulas in the case of discrete data, we adopt a "jittering" method for the claim counts. Elliptical copulas are proposed to accommodate the intertemporal dependency of the "jittered" claim counts, and thus the subject-specific heterogeneity on the frequency of claims. The resulting predictive distribution and the corresponding credibility of claim frequency are derived for ratemaking purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts in automobile insurance from a major insurer in Singapore. We demonstrate that the copula with "jittering" method outperforms several standard count regression models in the prediction.

PRESENTATION


Tim Verdonck (KU Leuven)

Robust covariance estimation for financial applications
(joint work with Mia Hubert and Peter Rousseeuw)

The Minimum Covariance Determinant (MCD) method (Rousseeuw, 1984) is a highly robust estimator of multivariate location and scatter. In addition to being highly resistant to outliers, the MCD is affine equivariant, i.e. the estimates behave properly under affine transformations of the data. Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rousseeuw and Van Driessen (1999) is used.
This algorithm starts by drawing a large number of random subsets and then takes so-called concentration steps to obtain a more accurate approximation to the MCD. The FASTMCD algorithm is affine equivariant but not permutation invariant.
In this presentation we propose a deterministic algorithm, denoted as DetMCD, which does not use random subsets and is even faster. It computes a small number of deterministic initial estimators, followed by concentration steps. The DetMCD algorithm is permutation invariant and very close to affine equivariant. The good performance of DetMCD is illustrated on some real data sets drawn from economics and finance.

Bibliography
Hubert, M., Rousseeuw, P.J. and Verdonck, T. (2011). A deterministic algorithm for robust location and scatter. Under review.
Rousseeuw, P.J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871-880.
Rousseeuw, P.J. and Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212-223.

PRESENTATION


Dacheng Xiu  (University of Chicago, Booth School of Business)

Dissecting and Deciphering European Option Prices using Closed-Form Series Expansion

We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using either the Hermite polynomial approach or the undetermined coefficients method. Departing from the usual option pricing routine in the literature, our model assumptions are fairly general, with no requirements for affine dynamics or explicit characteristic functions. Moreover, the closed-form expansions provide a distinct insight into how and on which order the model parameters affect option prices, in particular for close-to-maturity options. Such explicit formulae are advantageous over alternative numerical solutions of partial differential equations or simulation methods in regard to real-time calibration and hedging with contingent claims. With closed-form expansions, we explicitly translate model features into option prices, such as stochastic interest rate, mean-reverting drift, and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach.

PRESENTATION

 


Links to former workshops on LÚvy processes:

1. Applications of LÚvy Processes in Financial Mathematics; EURANDOM, Eindhoven, The Netherlands, June 22 - 23, 2001
    (no link available)

2. Exotic Option Pricing under Advanced LÚvy Models; EURANDOM,  Eindhoven, The Netherlands, May 3 - 4, 2004
    (no link available)

3. Credit Risk under LÚvy Models; ICMS, Edinburgh, The United Kingdom, September 19 - 21, 2006

4. Statistical Inference for LÚvy Processes with Applications to Finance; EURANDOM, Eindhoven, The Netherlands,  July 15 - 17, 2009
 

 


Practical information

Conference Location
The workshop location is EURANDOM,  Den Dolech 2, 5612 AZ Eindhoven, Laplace Building, 1st floor, LG 1.105.

EURANDOM is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).

For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm

Contact
For more information please contact Mrs. Patty Koorn,
Workshop officer of  EURANDOM

 

 

Sponsored by:

STAR
S
tochastics-Theoretical and Applied Research

 

 

Last updated 23-09-11,
by PK