Rüdiger Kiesel

The estimation of transition matrices for sovereign credit ratings

Rating transition matrices for sovereigns are an important input to risk management of portfolios of emerging market credit exposures. They are widely used both in credit portfolio management and to calculate future loss distributions for pricing purposes. However, few sovereigns and almost no low credit quality sovereigns have ratings histories longer than a decade, so estimating such matrices is difficult. This paper shows how one may combine information from sovereign defaults observed over a longer period and a broader set of countries to derive estimates of sovereign transition matrices.

Semi-parametric modelling in finance: theoretical foundations

Abstract The benchmark theory of mathematical finance is the Black-Scholes-Merton theory, based on Brownian motion as the driving noise process for asset prices. Here the distributions of returns of the assets in a portfolio are multivariate normal. The two most obvious limitations here concern symmetry and thin tails, neither being consistent with real data. The most common replacements for the multinormal are parametric—stable, generalized hyperbolic, variance gamma. In this paper we advocate the use of semi-parametric models for distributions, where the mean vector μ and covariance Σ are parametric components and the so-called density generator (function) g is the non-parametric component. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We show how the parametric cases can be treated in a unified, systematic way within the non-parametric framework and obtain the density generators for the most important cases.

The Structure of Credit Risk: spread volatility and ratings transitions

Knowing the relative riskiness of different types of credit exposure is important for policy-makers designing regulatory capital requirements and for firms allocating economic capital. This paper analyses the risk structure of credit exposures with different maturities and credit qualities. It focuses particularly on risks associated with (i) ratings transitions and (ii) spread changes for given ratings. The analysis shows that, for high-quality debt, most risk stems from spread changes. This is significant because several recently proposed credit risk models assume no spread risk.

A two-factor model for the electricity forward market

This paper provides a two-factor model for electricity futures that captures the main features of the market and fits the term structure of volatility. The approach extends the one-factor model of Clewlow and Strickland to a two-factor model and modifies it to make it applicable to the electricity market. We will particularly deal with the existence of delivery periods in the underlying futures. Additionally, the model is calibrated to options on electricity futures and its performance for practical application is discussed.

A semi-parametric approach to risk management

Abstract The benchmark theory of mathematical finance is the Black–Scholes–Merton (BSM) theory, based on Brownian motion as the driving noise process for stock prices. Here the distributions of financial returns of the stocks in a portfolio are multivariate normal. Risk management based on BSM underestimates tails. Hence estimation of tail behaviour is often based on extreme value theory (EVT). Here we discuss a semi-parametric replacement for the multivariate normal involving normal variance–mean mixtures. This allows a more accurate modelling of tails, together with various degrees of tail dependence, while (unlike EVT) the whole return distribution can be modelled. We use a parametric component, incorporating the mean vector μ and covariance matrix Σ, and a non-parametric component, which we can think of as a density on [0,∞), modelling the shape (in particular the tail decay) of the distribution. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We discuss efficient methods to estimate the parametric and non-parametric components of our model and provide an algorithm for simulating from such a model. We fit our model to several financial data series. Finally, we calculate value at risk (VaR) quantities for several portfolios and compare these VaRs to those obtained from simple multivariate normal and parametric mixture models.

On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

In recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published. In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems. Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential LA©vy model.

Modeling the Forward Surface of Mortality

Longevity risk constitutes an important risk factor for insurance companies and pension plans. For its analysis, but also for evaluating mortality-contingent structured financial products, modeling approaches allowing for uncertainties in mortality projections are needed. One model class that has attracted interest in applied research as well as among practitioners are forward mortality models, which are defined based on forecasts of survival probabilities as can be found in generation life tables and infer dynamics on the entire age/term structure, or forward surface, of mortality. However, thus far, there has been little guidance on identifying suitable specifications and their properties. The current paper provides a detailed analysis of forward mortality models driven by a finite-dimensional Brownian motion. In particular, after discussing basic properties, we present an infinite-dimensional formulation, and we examine the existence of finite-dimensional realizations for time-homogeneous deterministic...

Modelling asset returns with hyperbolic distributions

Publisher Summary This chapter discusses applications of the hyperbolic distributions in financial modeling. To model the everyday movement of ordinary quoted stocks under the market pressure of many agents, an infinite measure is appropriate. The mixture representation transfers to characteristic functions on taking the Fourier transform. Hyperbolic densities provide a good fit for a range of financial data, not only in the tails but throughout the distribution. The hyperbolic tails are log-linear: much fatter than normal tails but much thinner than stable ones. Under the assumptions of independence and identical distribution, a maximum likelihood analysis is performed. There is more mass around the origin and in the tails than the normal distribution suggests and that fitting returns to a hyperbolic distribution is to be preferred. By contrast, the hyperbolic approach is designed to give a reasonable fit throughout and in particular a better fit overall than the normal.

Tauberian theorems for general power series methods

Let us assume throughout that ( p n ) denotes a sequence of reals which satisfies For real sequences ( s n ) with increments a n = s n – s n−1 for n ≥ 0,(where s −1 = 0), we consider the power seriesmethod of summability ( P ), where we say The power series methods ( P ) containthe so-called ( J p )-methods ( R = 1)and the Borel-type methods ( B p )( R = ∞). We consider only regular ( P )-methods, i.e. s n → s implies s n → s ( P ). By theorem 5 in [5], p.49, we have regularity if and only if Here we are interested in the converse conclusion, namely s n → s ( P ) implies s n → s , which can only be validiffurther conditions, so-called Tauberian conditions are satisfied by ( s n ). These so-called Tauberian theorems for power series methods have a long history; see e.g. the books [ 5, 14, 23 ], and they found new attentionrecently in the papers [ 6, 18, 19, 20 ] and [ 8, 9, 10, 11, 12 ]. The latter papers contain certain o - Tauberian theorems for all power series methods in question and O -Tauberian theorems, if the weight sequence ( p n ) can be interpolated by alogarithmico-exponential function g (·)(see e.g. [ 4 ]), i.e.

An Extreme Analysis of VaRs for Emerging Market Benchmark Bonds

This paper examines the practical usefulness of Extreme Value Theory (EVT) techniques for estimating Value-at-Risk (VaR). Unlike most past studies, the performance of EVT estimators of empirical return distributions. We show that for confidence levels similar to those commonly used in market risk calculations, EVT and naive estimators yield almost identical results when applied to one-day emerging estimators yield different results on actual data but differences disappear in a Monte Carlo exercises assuming t-distributed return innovations.