Description

The course offers an overview of advanced statistical methods in quantitative finance and insurance which should be comprehensible for a graduate student in financial engineering as well as for an inexperienced newcomer who wants to get a grip on advanced statistical tools applied in these fields.

Course outline

The course consists naturally of a finance and insurance part. Each part contains lectures with high focus on practical applications. The finance starts with an introduction to stable distributions, which are the standard model for heavy tailed phenomena. Their numerical implementation is thoroughly discussed and applications to finance are given. Next lectures present the ideas of extreme value and copula analysis as applied to multivariate financial data. This topic is extended in the subsequent lectures which deal with tail dependence, a concept describing the limiting proportion that one margin exceeds a certain threshold given that the other margin has already exceeded that threshold. The next lectures review the market in catastrophe insurance risk, which emerged in order to facilitate the direct transfer of reinsurance risk associated with natural catastrophes from corporations, insurers, and reinsurers to capital market investors. The next part of the course employs functional data analysis for the estimation of smooth implied volatility surfaces. These surfaces are a result of using an oversimplified market benchmark model - the Black-Scholes formula - to real data. An attractive approach to overcome this problem is discussed when implied trinomial trees are applied to modeling implied volatilities and the corresponding state-price densities. An alternative route to tackling the implied volatility smile has led researchers to develop stochastic volatility models. The relative simplicity and the direct link of model parameters to the market makes Heston's model very attractive to front office users. Its application to FX option markets is covered in the next lectures. The following ones show how the computational complexity of stochastic volatility models can be overcome with the help of the Fast Fourier Transform. Afterwards the valuation of Mortgage Backed Securities is discussed in the course. The optimal prepayment policy is obtained via optimal stopping techniques. It is followed the topic of predicting corporate bankruptcy with Support Vector Machines. Next lectures present a novel approach to money-demand modeling using fuzzy clustering techniques. The first part of the course closes with productivity analysis for cost and frontier estimation. The nonparametric Data Envelopment Analysis is applied to efficiency issues of insurance agencies. The insurance part of the course starts with a lecture on loss distributions. The basic models for claim severities are introduced and their statistical properties are thoroughly explained. During next lectures, the methods of simulating and visualizing the risk process are discussed. This topic is followed by an overview of the approaches to approximating the ruin probability of an insurer. Both finite and infinite time approximations are presented. Some of these methods are extended during next lectures, where classical and anomalous diffusion approximations to ruin probability are discussed and extended to cases when the risk process exhibits good and bad periods. The last three topics are related to one of the most important aspects of the insurance business - premium calculation. First, the basic concepts including the pure risk premium and various safety loadings under different loss distributions are introduced. Calculation of a joint premium for a portfolio of insurance policies in the individual and collective risk models is discussed as well. The inclusion of deductibles into premium calculation is the next topic discussed. The last lectures of the insurance part deal with setting the appropriate level of insurance premium within a broader context of business decisions, including risk transfer through reinsurance and the rate of return on capital required to ensure solvability.

Literature

• Cizek, Härdle, Weron (2005) "Statistical Tools for Finance and Insurance" Springer Verlag.
  
• Härdle, Klinke, Müller (1999) "XploRe Learning Guide, Springer Verlag"
  
• Klugman, Panjer and Willmot (1998)Loss Models: From Data to Decisions, Joh Wiley & Sons.
  
• Härdle, Simar (2003)Applied Multivariate Statistical Analysis, Springer Verlag.
  
• Franke, Härdle, Hafner (2004)Statistics of Financial Markets, Springer Verlag.
  
• Härdle, Kleinow, Stahl (2002) Applied Quantitative Finance, Springer Verlag.
  
• Härdle, Hlavka, Klinke (2000) XploRe Application Guide, Springer Verlag.