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Market-Consistent Actuarial Valuation

Author: Mario V. Wüthrich

Publisher: Springer Science & Business Media

Published: 2010-09-02

Total Pages: 164

ISBN-13: 3642148522

It is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. However, there is a general agreement that the balance sheet of an insurance company should be measured in a consistent way. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in a consistent way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency.

Market-Consistent Actuarial Valuation

Author: Mario V. Wüthrich

Publisher: Springer

Published: 2016-10-22

Total Pages: 145

ISBN-13: 3319466364

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This is the third edition of this well-received textbook, presenting powerful methods for measuring insurance liabilities and assets in a consistent way, with detailed mathematical frameworks that lead to market-consistent values for liabilities. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency. Including updates on recent developments and regulatory changes under Solvency II, this new edition of Market-Consistent Actuarial Valuation also elaborates on different risk measures, providing a revised definition of solvency based on industry practice, and presents an adapted valuation framework which takes a dynamic view of non-life insurance reserving risk.

Market-Consistent Actuarial Valuation

Author: Mario Valentin Wüthrich

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 126

ISBN-13: 3540736425

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Presents powerful methods to measure liabilities and assets in the same way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors.

Financial Modeling, Actuarial Valuation and Solvency in Insurance

Author: Mario V. Wüthrich

Publisher: Springer Science & Business Media

Published: 2013-04-04

Total Pages: 438

ISBN-13: 3642313922

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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.

The Fair Value of Insurance Liabilities

Author: Irwin T. Vanderhoof

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 389

ISBN-13: 1475767323

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This book explores theoretical and practical implications of reflecting the fair value of liabilities for insurance companies. In addition, the contributions discuss the disclosure of these values to the financial and regulatory communities and auditing firms which are actually calculating this illusive but important variable. It combines contributions by distinguished practitioners from the insurance, accounting and finance fields, with those of prominent academics. One of the central themes of the collection is that adequate disclosure of the true economic value of insurance company liabilities is both possible and desirable. Wherever possible, the insurance valuation process is wedded with modern financial theory. For example, the use of option pricing theory is applied to insurance companies, where the true value of the firm's liabilities is a critical variable. Methods such as cash flow, earned profit and indirect discount are explored.

Market Consistency

Author: Malcolm Kemp

Publisher: John Wiley & Sons

Published: 2009-09-10

Total Pages: 647

ISBN-13: 0470684895

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Achieving market consistency can be challenging, even for the most established finance practitioners. In Market Consistency: Model Calibration in Imperfect Markets, leading expert Malcolm Kemp shows readers how they can best incorporate market consistency across all disciplines. Building on the author's experience as a practitioner, writer and speaker on the topic, the book explores how risk management and related disciplines might develop as fair valuation principles become more entrenched in finance and regulatory practice. This is the only text that clearly illustrates how to calibrate risk, pricing and portfolio construction models to a market consistent level, carefully explaining in a logical sequence when and how market consistency should be used, what it means for different financial disciplines and how it can be achieved for both liquid and illiquid positions. It explains why market consistency is intrinsically difficult to achieve with certainty in some types of activities, including computation of hedging parameters, and provides solutions to even the most complex problems. The book also shows how to best mark-to-market illiquid assets and liabilities and to incorporate these valuations into solvency and other types of financial analysis; it indicates how to define and identify risk-free interest rates, even when the creditworthiness of governments is no longer undoubted; and it explores when practitioners should focus most on market consistency and when their clients or employers might have less desire for such an emphasis. Finally, the book analyses the intrinsic role of regulation and risk management within different parts of the financial services industry, identifying how and why market consistency is key to these topics, and highlights why ideal regulatory solvency approaches for long term investors like insurers and pension funds may not be the same as for other financial market participants such as banks and asset managers.

Time-Consistent Actuarial Valuations

Author: Ahmad Salahnejhad Ghalehjooghi

Publisher:

Published: 2015

Total Pages: 38

ISBN-13:

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Time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. This method is applied to an insurance risk process in the form of a diffusion process and a jump process in order to capture the heavy tailed nature of insurance liabilities. We show that in the case of the diffusion process, the one-period time-consistent Variance premium principle converges to the non-linear exponential indifference price. Furthermore, we show that the Standard-Deviation and the Cost-of-Capital principle converge to the same price limit. Adding the jump risk gives a more realistic picture of the price. Furthermore, we no longer observe that the different premium principles converge to the same limit since each principle reflects the effect of the jump differently. In the Cost-of-Capital principle, in particular the VaR operator fails to capture the jump risk for small jump probabilities, and the time-consistent price depends on the distribution of the premium jump.

Implicit Embedded Options in Life Insurance Contracts

Author: Nils Rüfenacht

Publisher: Springer Science & Business Media

Published: 2012-05-04

Total Pages: 187

ISBN-13: 3790828424

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This book presents a market-consistent valuation framework for implicit embedded options in life insurance contracts. This framework is used to perform an empirical analysis based on more than 110,000 actual and in-force life insurance policies and with a focus on the modeling of interest rates. Its results are the answer to the central question posed in the objectives: What value do the embedded options and guarantees considered have? This question is answered both absolutely and relative to the current policy reserves, from the perspective of the insurer, the policyholder and the shareholder respectively

Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time

Author: Lukasz Delong

Publisher:

Published: 2018

Total Pages: 62

ISBN-13:

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We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the second step, the remaining part of the claim is valuated via an actuarial valuation. Then, we extend this approach to a multi-period setting by backward iterations for a given discrete-time step $h$, and consider the continuous-time limit for $h to 0$. We formally derive a partial differential equation for the valuation operator which satisfies the continuous-time limit of the multi-period, discrete-time iterations and prove that this valuation operator is actuarial and market-consistent. We show that our continuous-time fair valuation operator has a natural decomposition into the best estimate of the liability and a risk margin. The dynamic hedging strategy associated with the continuous-time fair valuation operator is also established. Finally, the valuation operator and the hedging strategy allow us to study the dynamics of the net asset value of the insurer.

Market Consistent and Sub-Consistent Valuations in Incomplete Markets

Author: Hirbod Assa

Publisher:

Published: 2015

Total Pages: 41

ISBN-13:

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From January 2016, all insurance companies that are regulated within Solvency II framework will have to value their asset and liabilities using a market-consistent method. This paper studies market-consistent and sub-consistent valuations in incomplete financial markets with two types (type I and II) of market consistency. While market consistency of type I holds under fairly weak assumptions, the type II consistency, which is the usual definition of market consistency in the literature, holds only if the market prices are linear for fully hedged assets. We also characterize the market consistent and sub-consistent evaluators in several different ways. We discuss how market-consistent and sub-consistent valuations can be regarded as a robust approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions.