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Preface | |
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About the Authors | |
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Introduction | |
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Organization of the Book | |
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References | |
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Probability and Statistics | |
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Discrete Probability Distributions | |
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Basic Concepts | |
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Discrete Probability Distributions Defined | |
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Bernoulli Distribution | |
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Binomial Distribution | |
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Poisson Distribution | |
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References | |
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Continuous Probability Distributions | |
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Continuous Random Variables and Probability Distributions | |
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The Normal Distribution | |
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Other Popular Distributions | |
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References | |
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Describing a Probability Distribution Function: Statistical Moments and Quantiles | |
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Location | |
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Dispersion | |
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Asymmetry | |
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Concentration in Tails | |
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Statistical Moments | |
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Quantiles | |
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Sample Moments | |
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Normal Distribution Revisited | |
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References | |
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Joint Probability Distributions | |
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Joint Probability Distributions Defined | |
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Marginal Distributions | |
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Dependence of Random Variables | |
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Multivariate Normal Distribution | |
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Elliptical Distributions | |
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References | |
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Copulas | |
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Drawbacks of Correlation | |
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Overcoming the Drawbacks of Correlation: Copulas | |
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Mathematical Definition of Copulas | |
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References | |
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Stable Distributions | |
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Properties of the Stable Distribution | |
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Considerations in the Use of the Stable Distribution | |
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Truncated Stable Distributions | |
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References | |
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Estimation Methodologies | |
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Fitting Probability Distributions by Maximum Likelihood Estimation | |
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Confidence Bounds | |
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Hypothesis Tests and P-Value | |
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Relationship between Hypothesis Tests and Confidence Bounds | |
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Fitting Stable Distributions | |
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Comparing Probability Distributions: Testing for the Goodness of Fit | |
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References | |
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Stochastic Processes | |
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Stochastic Processes in Discrete Time and Time Series Analysis | |
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Stochastic Processes in Discrete Time | |
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ARCH and GARCH Models | |
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ARMA-GARCH Illustration | |
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References | |
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Stochastic Processes in Continuous Time | |
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The Poisson Process | |
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Brownian Motion | |
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Stochastic Differential Equations | |
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Levy Processes | |
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References | |
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Portfolio Selection | |
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Equity and Bond Return Distributions | |
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Evidence from the U.S. Stock Market | |
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Evidence from the U.S. Bond Market | |
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References | |
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Risk Measures and Portfolio Selection | |
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Desirable Features of Investment Risk Measures | |
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Alternative Risk Measures for Portfolio Selection | |
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References | |
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Risk Measures in Portfolio Optimization and Performance Measures | |
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Efficient Frontiers and Return Distribution Assumption | |
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Portfolio Optimization and Conditional Value-at-Risk versus Value-at-Risk | |
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Performance Measures | |
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References | |
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Risk Management | |
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Market Risk | |
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Adoption of VaR for Measuring Market Risk | |
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VaR and Bank Capital Requirements | |
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Computation of VaR | |
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Evaluation of VaR Methods: Strengths and Weaknesses | |
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Stable Modeling of VaR | |
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Alternative to VaR: Expected Tail Loss | |
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References | |
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Coherent Risk Measures | |
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Credit Risk | |
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Credit Risk | |
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Credit Risk Framework for Banks: Basel I and Basel II | |
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Overview of Credit Risk Modeling | |
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Credit Risk Management Tools | |
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An Integrated Market and Credit Risk Management Framework Based on the Structural Approach | |
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An Integrated Market and Credit Risk Management Framework Based on the Intensity-Based Model | |
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Building An Econometric Model for the Intensity-Based Model | |
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References | |
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Operational Risk | |
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Operational Risk Defined | |
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Capital Requirement for Operational Risk | |
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Comparison of Market, Credit, and Operational Risk Distributions | |
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Aggregated Stochastic Models for Operational Risk | |
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References | |
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Option Pricing | |
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Introduction to Option Pricing and the Binomial Model | |
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Options Contracts | |
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Basic Components of the Option Price | |
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Boundary Conditions for the Price of an Option | |
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Discrete-Time Option Pricing: Binomial Model | |
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Convergence of the Binomial Model | |
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References | |
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Black-Scholes Option Pricing Model | |
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Motivation | |
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Black-Scholes Formula | |
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Computing a Call Option Price | |
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Sensitivity of Option Price to a Change in Factors: The Greeks | |
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Computing a Put Option Price | |
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Assumptions Underlying the Black-Scholes Model and Basic Extensions | |
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Black-Scholes Model Applied to the Pricing of Options on Bonds: Importance of Assumptions | |
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References | |
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Extension of the Black-Scholes Model and Alternative Approaches | |
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The "Smile Effect" | |
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Continuous-Time Models | |
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Discrete-Time Models | |
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References | |
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Index | |