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2013 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Financial Modeling, Actuarial Valuation and Solvency in Insurance

verfasst von: Mario V. Wüthrich, Michael Merz

Verlag: Springer Berlin Heidelberg

Buchreihe : Springer Finance

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments in this area in the financial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wüthrich combine ideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fully consistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options, dividend to shareholder questions, the role of re-insurance, etc.

This work embeds the solvency discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in the financial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a good background in probability theory and statistics, and should be familiar with popular distributions, stochastic processes, martingales, etc.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
In this chapter we give an introduction to financial modeling, actuarial valuation and solvency in insurance. The purpose of this book is to introduce sound risk measurement methods which form the bases of good risk management policies and solvency regulation in theory and in practice. In this book we define a comprehensive mathematical framework that adequately describes price formation and captures the corresponding risk factors that influence the stability of the financial industry. In particular, we develop quantitative risk management models and methods for insurance companies. These can be used for risk assessment, supervision and management of insurance companies. The models and methods that we describe are at the heart of quantitative solvency considerations of insurance companies and belong to the wider area of enterprise risk management. To fulfill this task we need to introduce the full balance sheet approach which is described in the present chapter. Moreover, we discuss solvency in general and we describe related general modeling issues. The chapter is closed by giving an overview of the topics treated in the book.
Mario V. Wüthrich, Michael Merz

Financial Valuation Principles

Frontmatter
Chapter 2. State Price Deflators and Stochastic Discounting
Abstract
In this chapter we describe stochastic discounting and valuation of random cash flows in a multiperiod discrete time setting. We therefore start by introducing the term structure of interest rates notion. We briefly discuss the calibration of the actual risk-free interest rate curve using the Svensson and the Nelson–Siegel term structure families. The main purpose of this chapter is then to introduce a consistent multiperiod pricing framework. This consistent multiperiod pricing framework is either based on state price deflators or on equivalent martingale measures which, in particular, lead to a pricing framework free of arbitrage. We introduce these concepts and describe their connection using the market price of risk construction. In fact, we insist of understanding price processes under both concepts (and their connection) because calibration, prediction and pricing consider both frameworks simultaneously.
Mario V. Wüthrich, Michael Merz
Chapter 3. Spot Rate Models
Abstract
In the previous chapter we have introduced the general valuation framework and state price deflators as abstract concepts. In this and the next chapters we present explicit models for state price deflator modeling. In the present chapter we consider models that are based on spot rates. They include multivariate Gaussian distributions and affine term structure models such as the discrete time one-factor and multifactor Vasicek models, ARMA and conditionally heteroscedastic time-series models, gamma spot rate models and the discrete time Black–Karasinski model. These models are supported by explicit applications to Swiss market financial data, and we analyze their strengths and weaknesses.
Mario V. Wüthrich, Michael Merz
Chapter 4. Stochastic Forward Rate and Yield Curve Modeling
Abstract
The state price deflators introduced in the previous chapter have several weaknesses such as they do not allow for sufficient modeling flexibility in practice and as they do not provide convincing fits to real data. In the present chapter we introduce the Heath–Jarrow–Morton (HJM) framework which is much more flexible and allows for potentially infinite dimensional term structure curves. Crucial in the HJM framework is the no-arbitrage condition which leads to the so-called HJM term that is analyzed in this chapter. We give explicit examples for the HJM framework in terms of the Cairns forward rate model and of the Teichmann–Wüthrich yield curve prediction model.
Mario V. Wüthrich, Michael Merz
Chapter 5. Pricing of Financial Assets
Abstract
This chapter closes the first part of the book which is on financial modeling and state price deflator construction. We give several examples of valuation of cash flows and basis financial instruments of the financial market, and we model and price defaultable bonds and derivatives of underlying financial instruments such as European put and call options. This provides the grounding for the valuation of insurance portfolios, in particular, if they include financial options such as minimal interest rate guarantees. Moreover, we define the Vasicek financial model which is going to be used as toy model in many subsequent examples.
Mario V. Wüthrich, Michael Merz

Actuarial Valuation and Solvency

Frontmatter
Chapter 6. Actuarial and Financial Modeling
Abstract
In this chapter we lay the basis for actuarial valuation. We introduce the notion of financial risk and insurance technical risk. Such a split is crucial because it explains which risks can be hedged at financial markets and which risks cannot be hedged and need to be absorbed by the insurance company. This will result in the split of the filtration into a financial filtration and an insurance technical filtration which describe the corresponding flow of information. Moreover, the previously introduced state price deflator receives a deeper meaning in terms of a financial deflator and a probability distortion. The former describes price formation at financial markets, the latter describes margins for non-hedgeable risks.
Mario V. Wüthrich, Michael Merz
Chapter 7. Valuation Portfolio
Abstract
In this chapter we introduce the valuation portfolio of Buchwalder–Bühlmann–Merz–Wüthrich. The valuation portfolio provides a systematic approach for replicating insurance liabilities by financial instruments, leaving only the non-hedgeable risks. The latter are replaced by so-called best-estimates. The valuation portfolio allows for the valuation of insurance cash flows, it describes the dynamical component called claims development result and it analyzes the inherit prediction uncertainties. This construction is supplemented by explicit examples in life and non-life insurance.
Mario V. Wüthrich, Michael Merz
Chapter 8. Protected Valuation Portfolio
Abstract
The valuation portfolio constructed in the previous chapter covers expected insurance liabilities and leads to best-estimate reserves for insurance liabilities. However to price insurance liabilities it is not sufficient to consider expected insurance liabilities. In general, a (risk averse) risk bearer of the insurance liabilities asks for an additional margin for settling the (non-hedgeable) insurance technical risks and for covering possible shortfalls in their development. The sum of the best-estimate reserves and this margin for non-hedgeable insurance technical risks then constitutes the so-called risk-adjusted reserves. In this chapter we give a methodological approach for the construction of risk-adjusted reserves. For this purpose we construct the protected valuation portfolio, which is a valuation portfolio protected against insurance technical risks. We give explicit numerical examples in terms of life and non-life insurance portfolios which provide interesting deeper insights. The core concept here is to choose appropriate probability distortions.
Mario V. Wüthrich, Michael Merz
Chapter 9. Solvency
Abstract
In this chapter we merge all available financial positions to the full balance sheet approach. To avoid inconsistencies it is crucial that the same state price deflator (and valuation method) is applied to all financial positions of the balance sheet. The solvency consideration then adds a dynamic component to the problem, namely, it considers the question whether the values of the liabilities are covered by asset values also in one year’s time from today. We start this chapter by introducing risk measures that analyze the dynamic question under stress scenarios. Then we define the notions of solvency and acceptability which are supplemented by many examples in asset-and-liability management. We discuss the limited liability option of shareholders, provide insight on dividend payment rules. We analyze hedging financial risk with the Margrabe option and we discuss portfolio optimization under solvency constraints.
Mario V. Wüthrich, Michael Merz
Chapter 10. Selected Topics and Examples
Abstract
We discuss open issues and give new results for dealing with these issues. We start off by discussing model and, in particular, parameter uncertainty. We describe how these can be dealt with in a solvency framework using Bayesian models. Then we describe cost-of-capital margin calculations as they are used in practice. We give some insight to dependence modeling (such as calendar year dependence in non-life insurance run-offs); we discuss premium liability modeling of new insurance business resulting in the notion of attritional and large claims; and we discuss risk mitigation using reinsurance.
Finally, the heart of this chapter (or even of the whole book) is the definition of a complete solvency model for a toy insurance company. We study the solvency position of this toy insurance company under various different management decisions.
Mario V. Wüthrich, Michael Merz

Appendix

Frontmatter
Chapter 11. Auxiliary Considerations
Abstract
This chapter can be viewed as appendix. We give results and proofs that are of broader interest. These include useful results for Gaussian distributions, change of numeraire technique, and pricing of European style options.
Mario V. Wüthrich, Michael Merz
Backmatter
Metadaten
Titel
Financial Modeling, Actuarial Valuation and Solvency in Insurance
verfasst von
Mario V. Wüthrich
Michael Merz
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-31392-9
Print ISBN
978-3-642-31391-2
DOI
https://doi.org/10.1007/978-3-642-31392-9