On robust estimation of the location parameter

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

Earnings Management and Investor Protection: An International Comparison

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the risk-neutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13) It has been well documented that return variance is stochastic. When investing in a security, an investor faces at least two sources of uncertainty, namely the uncertainty about the return as captured by the return variance, and the uncertainty about the return variance itself. It is important to know how investors deal with the uncertainty in return variance to effectively manage risk and allocate assets, to accurately price and hedge derivative securities, and to understand the behavior of financial asset prices in general. We develop a direct and robust method for quantifying the return variance risk premium on an asset using the market prices of options written on this asset. Our method uses the notion of a variance swap, which is an over-thecounter contract that pays the difference between a standard estimate of the realized variance and the fixed variance swap rate. Since variance swaps cost zero to enter, the variance swap rate represents the risk-neutral expected value of the realized variance. We show that the variance swap rate can be synthesized accurately by a particular linear combination of option prices. We propose to

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Variance Risk Premiums

We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi-closed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings. I. Introduction We identify and characterize a class of term structure models where bond yields are quadratic functions of the Markov process. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We identify the necessary and sufficient conditions for the quadratic class and consider the general asset pricing problem under the quadratic framework. In particular, we propose two transform methods to price a wide variety of interest rate derivatives in closed or semi-closed form. We further illustrate how the pricing methods can be applied to more general settings. Examples include option pricing for currencies or stocks with quadratic stochastic volatilities. Our interests in the quadratic class come mainly from concerns on empirical application. Recent empirical research within the affine framework of Duffie and Kan (1996) indicates an inherent tension between i) delivering good empirical performance in matching salient features of the interest rate data and ii) excluding positive probabilities of having negative interest rates. For example, Backus, Telmer, and Wu (1999) and Dai and Singleton (2000) find that incorporating Gaussian state variables in the affine framework significantly increases the flexibility for model design and greatly improves its empirical performance in capturing the conditional dynamics of interest rates. Dai and Singleton (2001)

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Asset Pricing under the Quadratic Class

This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies 2 stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index.

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The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments

https://doc.rero.ch/record/5228/files/1_fin0105.pdf

A geometric approach to multiperiod mean variance optimization of assets and liabilities

In this paper, we study the economic benefits from using credit scoring models. We contribute to the literature by relating the discriminatory power of a credit scoring model to the optimal credit decision. Given the Receiver Operating Characteristic (ROC) curve of the credit scoring model, we derive a) the profit-maximizing cuttoff regime and b) the pricing curve. In addition, we study a stylized loan market model with banks that differ in the quality of their credit scoring model. We find that profitability varies substantially among lenders. More powerful credit scoring models lead to economically significant differences in credit portfolio performance.

Economic Benefit of Powerful Credit Scoring

We propose a new modeling framework to study the asset pricing implications of learning under ambiguity aversion. In a continuous time partial information Lucas economy, we characterize analytically equilibrium equity returns and make the following observations. First, learning under ambiguity aversion implies an equilibrium discount for ambiguity, if and only if relative risk aversion is below one or, equivalently, the elasticity of intertemporal substitution (EIS) is above one. In this case, ambiguity aversion increases conditional equity premia and volatilities. Second, equilibrium interest rates are lower, irrespective of risk aversion. Third, no time-invariant relation between excess returns and conditional variances exists. Therefore, estimated relations between excess returns and equity conditional variances are highly time varying and have an indeterminate sign. Fourth, estimates of the EIS based on standard Euler equations for equity returns are strongly downward biased in a setting of learning and ambiguity aversion. Therefore, an EIS well above one can be consistent with estimates of EIS well below one. Fifth, ambiguity does not resolve asymptotically. Finally, using realistic model parameters, we show that a low risk aversion and a moderate amount of ambiguity are consistent with the equity premium, the low interest rate, and the excess volatility puzzles.

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Markus Leippold

Papers

Asset Pricing under the Quadratic Class

The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments

A geometric approach to multiperiod mean variance optimization of assets and liabilities

Economic Benefit of Powerful Credit Scoring

Learning and Asset Prices under Ambiguous Information