Ebook: Applied Quantitative Finance

Recent years have witnessed a growing importance of quantitative methods in both financial research and industry. This development requires the use of advanced techniques on a theoretical and applied level, especially when it comes to the quantification of risk and the valuation of modern financial products. Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance. Themes that are dominant in current research and which are presented in this book include among others the valuation of Collaterized Debt Obligations (CDOs), the high-frequency analysis of market liquidity, the pricing of Bermuda options and realized volatility. All Quantlets for the calculation of the given examples are downloadable from the Springer web pages.

Table of Contents

Cover

Applied Quantitative Finance, Second Edition

ISBN: 9783540691778 eISBN: 9783540691792

Preface to the 2nd Edition

Preface to the 1st Edition

Contents

Contributors

Frequently Used Notation

1 Modeling Dependencies with Copulae

1.1 Introduction
1.2 Bivariate Copulae
1.2.1 Copula Families
o Simplest Copulae
o Elliptical Family
o Archimedean Family
1.2.2 Dependence Measures
1.3 Multivariate Copulae
1.3.1 Copula Families
o Archimedean and Hierarchical Archimedean copulae
1.3.2 Dependence Measures
o Generalizations
1.4 Estimation Methods
Parametric margins
Canonical Maximum Likelihood
1.5 Goodness-of-Fit Tests for Copulae
1.6 Simulation Methods
1.6.1 Conditional Inverse Method
1.6.2 Marshal-Olkin Method
1.7 Applications to Finance
1.7.1 Asset Allocation
1.7.2 Value-at-Risk
1.7.3 Time Series Modeling
1.8 Simulation Study and Empirical Results
1.8.1 Simulation Study
o Setup of the study
o Discussion of the results
1.8.2 Empirical Example
1.9 Summary
Bibliography

2 Quantification of Spread Risk by Means of Historical Simulation

2.1 Introduction
2.2 Risk Categories - a Definition of Terms
2.3 Yield Spread Time Series
2.3.1 Data Analysis
2.3.2 Discussion of Results
2.4 Historical Simulation and Value at Risk
2.4.1 Risk Factor: Full Yield
2.4.2 Risk Factor: Benchmark
2.4.3 Risk Factor: Spread over Benchmark Yield
2.4.4 Conservative Approach
2.4.5 Simultaneous Simulation
2.5 Mark-to-Model Backtesting
2.6 VaR Estimation and Backtesting
2.7 P-P Plots
2.8 Q-Q Plots
2.9 Discussion of Simulation Results
2.9.1 Risk Factor: Full Yield
2.9.2 Risk Factor: Benchmark
2.9.3 Risk Factor: Spread over Benchmark Yield
2.9.4 Conservative Approach
2.9.5 Simultaneous Simulation
2.10 Internal Risk Models
Bibliography

3 A Copula-Based Model of the Term Structure of CDO Tranches

3.1 Introduction
3.2 A Copula-Based Model of Basket Credit Losses Dynamics
3.3 Stochastic Processes with Dependent Increments
3.4 An Algorithm for the Propagation of Losses
3.5 Empirical Analysis
3.6 Concluding Remarks
Bibliography

4 VaR in High Dimensional Systems - a Conditional Correlation Approach

4.1 Introduction
4.2 Half-Vec Multivariate GARCH Models
4.3 Correlation Models
4.3.1 Motivation
4.3.2 Log-Likelihood Decomposition
4.3.3 Constant Conditional Correlation Model
4.3.4 Dynamic Conditional Correlation Model
4.3.5 Inference in the Correlation Models
4.3.6 Generalizations of the DCC Model
4.4 Value-at-Risk
4.5 An Empirical Illustration
4.5.1 Equal and Value Weighted Portfolios
4.5.2 Estimation Results
Bibliography

5 Rating Migrations

5.1 Rating Transition Probabilities
5.1.1 From Credit Events to Migration Counts
5.1.2 Estimating Rating Transition Probabilities
5.1.3 Dependent Migrations
5.1.4 Computational Aspects
5.2 Analyzing the Time-Stability of Transition Probabilities
5.2.1 Aggregation over Periods
5.2.2 Testing the Time-Stability of Transition Probabilities
5.2.3 Example
5.2.4 Computational Aspects
5.3 Multi-Period Transitions
5.3.1 Homogeneous Markov Chain
5.3.2 Bootstrapping Markov Chains
5.3.3 Rating Transitions of German Bank Borrowers
5.3.4 Portfolio Migration
5.3.5 Computational Aspects
Bibliography

6 Crossand Autocorrelation in Multi-Period Credit Portfolio Models

6.1 Introduction
6.2 The Models
6.2.1 A Markov-Chain Credit Migration Model
6.2.2 The Correlated-Default-Time Model
6.2.3 A Discrete Barrier Model
6.2.4 The Time-Changed Barrier Model
6.3 Inter-Temporal Dependency and Autocorrelation
6.4 Conclusion
Bibliography

7 Risk Measurement with Spectral Capital Allocation

7.1 Introduction
7.2 Review of Coherent Risk Measures and Allocation
7.2.1 Coherent Risk Measures
7.2.2 Spectral Risk Measures
7.2.3 Coherent Allocation Measures
7.2.4 Spectral Allocation Measures
7.3 Weight Function and Mixing Measure
7.4 Risk Aversion
7.5 Implementation
7.5.1 Mixing Representation
7.5.2 Density Representation
7.6 Credit Portfolio Model
7.7 Examples
7.7.1 Weighting Scheme
7.7.2 Concrete Example
7.8 Summary
Bibliography

8 Valuation and VaR Computation for CDOs Using Stein s Method

8.1 Introduction
8.1.1 A Primer on CDO
8.1.2 Factor Models
8.1.3 Numerical Algorithms
8.2 First Order Gauss-Poisson Approximations
8.2.1 Stein s Method the Normal Case
8.2.2 First-Order Gaussian Approximation
8.2.3 Stein s Method the Poisson Case
8.2.4 First-Order Poisson Approximation
8.3 Numerical Tests
8.3.1 Validity Domain of the Approximations
8.3.2 Stochastic Recovery Rate Gaussian Case
8.3.3 Sensitivity Analysis
8.4 Real Life Applications
8.4.1 Gaussian Approximation
8.4.2 Poisson Approximation
8.4.3 CDO Valuation
8.4.4 Robustness of VaR Computation
o Generating VaR Scenarios
o Stylized Portfolio Description
o Error Computation
Bibliography

9 Least Squares Kernel Smoothing of the Implied Volatility Smile

9.1 Introduction
9.2 Least Squares Kernel Smoothing of the Smile
9.3 Application
9.3.1 Weighting Functions, Kernels, and Minimization Scheme
9.3.2 Data Description and Empirical Demonstration
Bibliography
9.4 Proofs

10 Numerics of Implied Binomial Trees

10.1 Construction of the IBT
10.1.1 The Derman and Kani Algorithm
10.1.2 Compensation
10.1.3 Barle and Cakici Algorithm
10.2 A Simulation and a Comparison of the SPDs
10.2.1 Simulation Using the DK Algorithm
10.2.2 Simulation Using the BC Algorithm
10.2.3 Comparison with the Monte-Carlo Simulation
10.3 Example - Analysis of EUREX Data
Bibliography

11 Application of Extended Kalman Filter to SPD Estimation

11.1 Linear Model
11.1.1 Linear Model for Call Option Prices
11.1.2 Estimation of State Price Density
11.1.3 State-Space Model for Call Option Prices
11.2 Extended Kalman Filter and Call Options
11.3 Empirical Results
11.3.1 Extended Kalman Filtering in Practice
11.3.2 SPD Estimation in 1995
11.3.3 SPD Estimation in 2003
11.4 Conclusions
Bibliography

12 Stochastic Volatility Estimation Using Markov Chain Simulation

12.1 The Standard Stochastic Volatility Model
12.2 Extended SV Models
12.2.1 Fat Tails and Jumps
o The SVt Model
o The SV Model with Jump Components
12.2.2 The Relationship Between Volatility and Returns
o The SV-in-Mean Model
o The Asymmetric SV Model
12.2.3 The Long Memory SV Model
12.3 MCMC-Based Bayesian Inference
12.3.1 Bayes Theorem and the MCMC Algorithm
12.3.2 MCMC-Based Estimation of the Standard SV Model
12.4 Empirical Illustrations
12.4.1 The Data
12.4.2 Estimation of SV Models
12.5 Appendix
12.5.1 Derivation of the Conditional Posterior Distributions
Bibliography

13 Measuring and Modeling Risk Using High-Frequency Data

13.1 Introduction
13.2 Market Microstructure E ects
13.3 Stylized Facts of Realized Volatility
13.4 Realized Volatility Models
13.5 Time-Varying Betas
13.5.1 The Conditional CAPM
13.5.2 Realized Betas
13.6 Summary
Bibliography

14 Valuation of Multidimensional Bermudan Options

14.1 Introduction
14.2 Model Assumptions
14.3 Methodology
14.4 Examples
14.5 Conclusion
Bibliography

15 Multivariate Volatility Models

15.1 Introduction
15.1.1 Model Specifications
15.1.2 Estimation of the BEKK-Model
15.2 An Empirical Illustration
15.2.1 Data Description
15.2.2 Estimating Bivariate GARCH
15.2.3 Estimating the (Co)Variance Processes
15.3 Forecasting Exchange Rate Densities
Bibliography

16 The Accuracy of Long-term Real Estate Valuations

16.1 Introduction
16.2 Implementation
16.2.1 Computation of the Valuations
16.2.2 Data
16.3 Empirical Results
16.3.1 Characterization of the Test Market
16.3.2 Horse Race
16.4 Conclusion
Bibliography

17 Locally Time Homogeneous Time Series Modelling

17.1 Introduction
17.2 Model and Setup
17.2.1 Conditional Heteroskedastic Model
17.2.2 Parametric and Local Parametric Estimation and
Inference
17.2.3 Nearly Parametric Case
17.3 Methods for the Estimation of Parameters
17.3.1 Sequence of Intervals
17.3.2 Local Change Point Selection
17.3.3 Local Model Selection
17.3.4 Stagewise Aggregation
17.4 Critical Values and Other Parameters
17.5 Applications
17.5.1 Forecasting Performance for One and Multiple Steps
17.5.2 Value-at-Risk
17.5.3 A Multiple Time Series Example
Bibliography

18 Simulation Based Option Pricing

18.1 Introduction
18.2 The Consumption Based Processes
18.2.1 The Snell Envelope
18.2.2 The Continuation Value, the Continuation and Exercise
Regions
18.2.3 Equivalence of American Options to European Ones with
Consumption Processes
18.2.4 Upper and Lower Bounds Using Consumption Processes
18.2.5 Bermudan Options
18.3 The Main Procedure
18.3.1 Local Lower Bounds
18.3.2 The Main Procedure for Constructing Upper Bounds for
the Initial Position (Global Upper Bounds)
18.3.3 The Main Procedure for Constructing Lower Bounds for
the Initial Position (Global Lower Bounds)
18.3.4 Kernel Interpolation
18.4 Simulations
18.4.1 Bermudan Max Calls on d Assets
18.4.2 Bermudan Basket-Put
18.5 Conclusions
Bibliography

19 High-Frequency Volatility and Liquidity

19.1 Introduction
19.2 The Univariate MEM
19.3 The Vector MEM
19.4 Statistical Inference
19.5 High-Frequency Volatility and Liquidity Dynamics
Bibliography

20 Statistical Process Control in Asset Management

20.1 Introduction
20.2 Review of Statistical Process Control Concepts
20.3 Applications of SPC in Asset Management
20.3.1 Monitoring Active Portfolio Managers
20.3.2 Surveillance of the Optimal Portfolio Proportions
20.4 Summary
Bibliography

21 Canonical Dynamics Mechanism of Monetary Policy and Interest Rate

21.1 Introduction
21.2 Statistical Technology
21.3 Principles of the Fed Funds Rate Decision-Making
21.3.1 Fairness of In"ation Gauge
21.3.2 Neutral Interest Rate Based on Fair Gauge of In"ation
21.3.3 Monetary Policy-Making as Tight-Accommodative Cycles
Along Neutral Level as Dynamic Principal
21.4 Response Curve Structure and FOMC Behavioral Analysis
21.4.1 Data Analysis and Regressive Results
21.4.2 The Structure of the FOMC s Response Curve - Model
Characteristics, Interpretations
21.4.3 The Dynamics of the FFR - Model Implications
21.4.4 General Dynamic Mechanism for Long-Run Dependence of
Interest Rate and In"ation
21.5 Discussions and Conclusions
Bibliography

Index