Torsten Kleinow

Applied Quantitative Finance

Value at Risk.- Modeling Dependencies with Copulae.- Quantification of Spread Risk by Means of Historical Simulation.- A Copula-Based Model of the Term Structure of CDO Tranches.- VaR in High Dimensional Systems - a Conditional Correlation Approach.- Credit Risk.- Rating Migrations.- Cross- and Autocorrelation in Multi-Period Credit Portfolio Models.- Risk Measurement with Spectral Capital Allocation.- Valuation and VaR Computation for CDOs Using Steins Method.- Implied Volatility.- Least Squares Kernel Smoothing of the Implied Volatility Smile.- Numerics of Implied Binomial Trees.- Application of Extended Kalman Filter to SPD Estimation.- Stochastic Volatility Estimation Using Markov Chain Simulation.- Measuring and Modeling Risk Using High-Frequency Data.- Valuation of Multidimensional Bermudan Options.- Econometrics.- Multivariate Volatility Models.- The Accuracy of Long-term Real Estate Valuations.- Locally Time Homogeneous Time Series Modelling.- Simulation Based Option Pricing.- High-Frequency Volatility and Liquidity.- Statistical Process Control in Asset Management.- Canonical Dynamics Mechanism of Monetary Policy and Interest Rate.

Semiparametric Bootstrap Approach to Hypothesis Tests and Confidence Intervals for the Hurst Coefficient

A major application of rescaled adjusted range analysis (R–S analysis) is to the study of price fluctuations in financial markets. There, the value of the Hurst constant, H, in a time series may be interpreted as an indicator of the irregularity of the price of a commodity, currency or similar quantity. Interval estimation and hypothesis testing for H are central to comparative quantitative analysis. In this paper we propose a new bootstrap, or Monte Carlo, approach to such problems. Traditional bootstrap methods in this context are based on fitting a process chosen from a wide but relatively conventional range of discrete time series models, including autoregressions, moving averages, autoregressive moving averages and many more. By way of contrast we suggest simulation using a single type of continuous-time process, with its fractal dimension. We provide theoretical justification for this method, and explore its numerical properties and statistical performance by application to real data on commodity prices and exchange rates.

Web quantlets for time series analysis

New and advanced methods for nonlinear time series analysis are in general not available in standard software packages. Their implementation requires substantial time, computing power as well as programming skills. In time series analysis such a scenario is given by a recently suggested nonparametric lag selection procedure for univariate nonlinear autoregressive models which is based on the Corrected Asymptotic Final Prediction Error. In this paper we suggest a worldwide Web based specific client/server architecture that provides empirical researchers with fast access to new methods and powerful computing environments without knowing the statistical computing language and the server location. This architecture is implemented using the XploRe Quantlet technology and illustrated for nonparametric lag selection. Access to the Quantlet computing service can be obtained via standard WWW browsers or a Java client. The XploRe Quantlet service can be helpful in constructing research books and interactive teaching environments as the electronic version of this paper, available from http://ise.wiwi.hu-berlin.de/∼rolf/webquant.pdf, demonstrates.

Mortality and smoking prevalence: An empirical investigation in ten developed countries

We investigate the link between death rates and smoking prevalence in ten developed countries with the aim of using smoking prevalence data to explain differences in country-specific death rates. A particular problem in building a stochastic mortality model based on smoking prevalence is that there are in general no separate mortality data for smokers and non-smokers available. We show how we can estimate mortality rates for smokers and non-smokers using information about the smoking prevalence in a number of developed countries, and making an additional assumption about the death rates of smokers. We consider this empirical investigation to be the first step towards a consistent mortality model for multiple populations, which will require modelling of country specific differences in mortality, as well as non-smokers’ and smokers’ mortality rates.

Yet More on a Stochastic Economic Model: Part 1: Updating and Refitting, 1995 to 2009

Abstract In this paper we review the Wilkie asset model for a variety of UK economic indices, including the Retail Prices Index, both without and with an ARCH model, the wages index, share dividend yields, share dividends and share prices, long term bond yields, short term bond yields and index-linked bond yields, in each case by updating the parameters to June 2009. We discuss how the model has performed from 1994 to 2009 and estimate the values of the parameters and their confidence intervals over various sub-periods to study their stability. Our analysis shows that the residuals of many of the series are much fatter-tailed than in a normal distribution. We observe also that besides the stochastic uncertainty built into the model by the random innovations there is also parameter uncertainty arising from the estimated values of the parameters.

Semiparametric diffusion estimation and application to a stock market index

The analysis of diffusion processes in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A new model for a stock market index process is proposed in which the index is decomposed into an average growth process and an ergodic diffusion. The ergodic diffusion part of the model is not directly observable. A methodology is developed for estimating and testing the coefficient functions of this unobserved diffusion process. The estimation is based on the observations of the index process and uses semiparametric and non-parametric techniques. The testing is performed via the wild bootstrap resampling technique. The method is illustrated on S&P 500 index data.

Multi-population mortality models: fitting, forecasting and comparisons

We review a number of multi-population mortality models: variations of the Li & Lee model, and the common-age-effect (CAE) model of Kleinow. Model parameters are estimated using maximum likelihood. Although this introduces some challenging identifiability problems and complicates the estimation process it allows a fair comparison of the different models. We propose to solve these identifiability problems by applying two-dimensional constraints over the parameters. Using data from six countries, we compare and rank, both visually and numerically, the models’ fitting qualities and develop forecasting models that produce non-diverging, joint mortality rate scenarios. It is found that the CAE model fits best. But we also find that the Li and Lee model potentially suffers from robustness problems when calibrated using maximum likelihood.

Testing the diffusion coefficient

In mathematical finance diffusion models are widely used and a variety of different parametric models for the drift and diffusion coefficient coexist in the literature. Since derivative prices depend on the particular parametric model of the diffusion coefficient function of the underlying, a misspecification of this function leads to misspecified option prices. We develop two tests about a parametric form of the diffusion coefficient. The finite sample properties of the tests are investigated in a simulation study and the tests are applied to the 7 -day Eurodollar rate, the German stock market index DAX and five German stocks. For all observed processes, we find in the empirical analysis that our tests reject all tested parametric models. We conclude that affine diffusion processes might not be appropriate to model the evolution of financial time series and that a successful model for a financial market should incorporate the history of the observed processes of additional sources of randomness like stochastic volatility models.

Parameter risk in time-series mortality forecasts

Abstract The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland.

Pension Fund Management and Conditional Indexation

Conditional indexation offers a middle way between defined benefit and defined contribution pension schemes. In this paper, we consider a fully-funded pension scheme with conditional indexation. We show how the pension fund can be managed to reduce the risks associated with promised pension benefits when declared benefits are adjusted regularly during the working life. In particular, we derive an investment strategy that provides protection against underfunding at retirement and which is self-financing on average. Our results are illustrated in an extensive simulation study.