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Format: 1 Online-Ressource (X, 449 Seiten, 68 illus., 43 illus. in color)

ISBN: 9783319334462 , 9783319334455

Series Statement: Springer proceedings in mathematics & statistics volume 165

Language: English

Keywords: Finanzinnovation ; Zinsänderungsrisiko ; Finanzmathematik ; Konferenzschrift ; Konferenzschrift

DOI: 10.1007/978-3-319-33446-2

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Author information: Scherer, Matthias

Author information: Zagst, Rudi 1961-

Author information: Glau, Kathrin

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Format: 1 online resource (xi, 438 pages) : , illustrations; digital, PDF file(s).

Edition: 1st ed. 2015.

ISBN: 9783319091143 (ebook)

Series Statement: Springer Proceedings in Mathematics & Statistics, 99

Content: Quantitative models are omnipresent –but often controversially discussed– in todays risk management practice. New regulations, innovative financial products, and advances in valuation techniques provide a continuous flow of challenging problems for financial engineers and risk managers alike. Designing a sound stochastic model requires finding a careful balance between parsimonious model assumptions, mathematical viability, and interpretability of the output. Moreover, data requirements and the end-user training are to be considered as well. The KPMG Center of Excellence in Risk Management conference Risk Management Reloaded and this proceedings volume contribute to bridging the gap between academia –providing methodological advances– and practice –having a firm understanding of the economic conditions in which a given model is used. Discussed fields of application range from asset management, credit risk, and energy to risk management issues in insurance. Methodologically, dependence modeling, multiple-curve interest rate-models, and model risk are addressed. Finally, regulatory developments and possible limits of mathematical modeling are discussed.

Note: Bibliographic Level Mode of Issuance: Monograph , Part I Markets, Regulation, and Model Risk -- A Random Holding Period Approach for Liquidity-Inclusive Risk Management -- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models -- Model Risk in Incomplete Markets with Jumps -- Part II Financial Engineering -- Bid-Ask Spread for Exotic Options Under Conic Finance -- Derivative Pricing Under the Possibility of Long Memory in the supOU Stochastic Volatility Model -- A Two-Sided BNS Model for Multicurrency FX Markets -- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors -- Copula-Specific Credit Portfolio Modeling -- Implied Recovery Rates—Auctions and Models -- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence -- Part III Insurance Risk and Asset Management -- Participating Life Insurance Contracts Under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design -- Reducing Surrender Incentives Through Fee Structure in Variable Annuities -- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment -- Risk Control in Asset Management: Motives and Concepts -- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash -- Improving Optimal Terminal Value Replicating Portfolios -- Part IV Computational Methods for Risk Management -- Risk and Computation -- Extreme Value Importance Sampling for Rare Event Risk Measurement -- A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function -- Computation of Copulas by Fourier Methods -- Part V Dependence Modelling -- Goodness-of-fit Tests for Archimedean Copulas in High Dimensions -- Duality in Risk Aggregation -- Some Consequences of the Markov Kernel Perspective of Copulas -- Copula Representations for Invariant Dependence Functions -- Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection. , Also available in print form. , English

Additional Edition: Print version: ISBN 9783319091136

Language: English

DOI: 10.1007/978-3-319-09114-3

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Format: 1 online resource (469 pages)

ISBN: 981-327-256-2 , 981-327-255-4

Content: This book covers recent developments in the interdisciplinary fields of actuarial science, quantitative finance, risk- and asset management. The authors are leading experts from academia and practice who participated in Innovations in Insurance, Risk- and Asset Management, an international conference held at the Technical University of Munich in 2017. The topics covered include the mathematics of extreme risks, systemic risk, model uncertainty, interest rate and hybrid models, alternative investments, dynamic investment strategies, quantitative risk management, asset liability management, liability driven investments, and behavioral finance. This timely selection of topics is highly relevant for the financial industry and addresses current issues both from an academic as well as from a practitioner's point of view.

Note: Intro -- Contents -- Foreword -- Preface -- About the Editors -- Part I. Innovations in Risk Management -- 1. Behavioral Value Adjustments for Mortgage Valuation -- 1. Introduction -- 2. Literature review -- 3. A general framework for modeling behavioral risk -- 3.1. Defining behavioral risk -- 3.2. A general framework in parallel with credit risk -- 3.3. Behavioral risk adjustments -- 3.4. A general formula for portfolio valuation -- 4. Mortgage portfolio valuation with BIX model -- 4.1. Heterogeneity and granularity -- 4.2. Market factors -- 4.3. Exogenous factors -- 4.4. Marginal exercise probabilities -- 4.5. Hints for calibration -- 4.6. Survival exercise probabilities -- 4.7. Portfolio pricing -- 4.7.1. Expression for II0(X) -- 4.7.2. Expression for II1(X) -- 4.7.3. Expression for II2(X) -- 4.8. Simulation -- 5. Conclusion -- 6. Appendix -- References -- 2. Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Optionsin Default Intensity Models -- 1. Introduction -- 2. Call and put risk-neutral dynamics -- 3. Expected positive exposures under no WWR -- 4. Expected positive exposures under WWR -- 5. Proxys of ts -- 5.1. Q-expectation -- 5.2. Approximation of QCT -expectation -- 6. Potential future exposures (PFE) -- 7. Numerical experiments -- 8. Conclusion -- References -- 3. Consistent Iterated Simulation of Multivariate Defaults: Markov Indicators, Lack of Memory, Extreme-Value Copulas, and the Marshall- Olkin Distribution -- 1. Introduction -- 1.1. Problem one: "Survival-of-all" events -- 1.2. Problem two: "Mixed default/survival" events -- 1.3. Structure of the paper -- 2. Default-time distributions and survival-indicator processes -- 2.1. Markovian survival indicator-processes -- 2.2. Lack-of-memory properties -- 3. Problem one: Iterating "survival-of-all -- 3.1. Lack-of-memory properties revisited. , 3.2. Change in dependence when iterating non-self chaining copulas -- 4. Problem two: "Mixed default/survival" events -- 4.1. The looping default model and the Freund distribution -- 4.2. Marshall-Olkin distributions -- 4.3. Case study: Iteration bias for selected multivariate distributions -- 5. Conclusions -- Appendix A. Alternative construction of Markovian processes -- Acknowledgments -- References -- 4. Examples of Wrong-Way Risk in CVA Induced by Devaluations on Default -- 1. Introduction -- 1.1. Overview of the modeling framework -- 2. A PDE approach for both FX-driven and equity-driven WWR -- 2.1. FX -- 2.1.1. No-arbitrage drift for the market risk-factor (FX) -- 2.1.2. Final conditions - CVA payoff -- 2.2. Equity -- 2.2.1. No-arbitrage drift for the market risk-factor (equity) -- 2.2.2. Final conditions - CVA payoff -- 3. A structural approach for equity/credit WWR -- 3.1. AT1P -- 3.1.1. Credit risk -- 3.1.2. Equity price -- 3.2. Introducing WWR -- 4. Results -- 4.1. Models calibrations -- 4.2. Equity WWR: Correlation impact -- 4.3. Equity WWR: Devaluation impact -- 4.4. FX WWR: FX Vega -- 5. Conclusions -- References -- 5. Implied Distributions from Risk-Reversals and Brexit/Trump Predictions -- 1. Introduction -- 2. Literature Review -- 3. Method -- 4. Results -- 4.1. 2016 Brexit referendum -- 4.2. 2016 US election - Trump -- 4.3. 2017 French elections -- 4.4. 2017 UK general election -- 5. Conclusions -- References -- 6. Data and Uncertainty in Extreme Risks: A Nonlinear Expectations Approach -- 1. Introduction -- 2. DR-expectations -- 2.1. Data-robust risk measures -- 3. Regularization from data -- 4. Heavy tails -- 4.1. Expected shortfall -- 4.2. Value at risk -- 4.3. Probability of loss -- 4.4. Integrated tail and Cramer-Lundberg failure probability -- 4.5. Distortion risk -- Appendix -- Acknowledgments -- References. , 7. Intrinsic Risk Measures -- 1. Introduction -- 2. Terminology and preliminaries -- 2.1. Acceptance sets -- 2.2. Traditional risk measures -- 2.2.1. Coherent risk measures -- 2.2.2. Convex risk measures -- 2.2.3. Cash-subadditivity and quasi-convexity of risk measures -- 2.2.4. General monetary risk measures -- 3. Intrinsic risk measures -- 3.1. Fundamental concepts -- 3.2. Representation on conic acceptance sets -- 3.3. Efficiency of the intrinsic approach -- 3.4. Dual representations on convex acceptance sets -- 4. Conclusion -- Bibliography -- 8. Pathwise Construction of Affine Processes -- 1. Introduction -- 2. Preliminaries -- 2.1. Notation -- 2.2. Affine processes -- 2.3. Towards the multivariate Lamperti transform -- 2.4. Affine processes of Heston type -- 3. Existence of the solution of the time-change equation -- 3.1. The setting -- 3.2. The core of the proof -- 3.2.1. Approximation of the vector field -- 3.2.2. The algorithm -- 4. Pathwise construction of affine processes with time-change -- Bibliography -- Part II. Innovations in Insurance and Asset Management -- 9. Fixed-Income Returns from Hedge Funds with Negative Fee Structures: Valuation and Risk Analysis -- 1. Introduction -- 2. Hedge fund fee structures: From traditional fee structures to negative fees -- 2.1. Traditional fee structures -- 2.2. From first-loss to negative first-loss fee structure -- 3. Pricing the payoffs -- 4. Risk analysis of the investor's position as a bond -- 4.1. Impact of the manager's deposit c -- 5. Conclusion -- References -- 10. Static Versus Adapted Optimal Execution Strategies in Two Benchmark Trading Models -- 1. Introduction -- 2. Discrete time trading with information flow -- 2.1. Model formulation with cost based criterion -- 2.2. Permanent market impact: Optimal adapted solution -- 2.3. Permanent market impact: Optimal deterministic solution. , 2.4. Permanent market impact: Adapted vs deterministic solution -- 3. Continuous time trading with risk function -- 3.1. Model formulation with cost and risk based criterion -- 3.2. Optimal adapted solution under temporary and permanent impact -- 3.3. Optimal static solution under temporary and permanent impact -- 3.4. Comparison of optimal static and adapted solutions -- 4. Conclusions and further research -- References -- 11. Liability Driven Investments with a Link to Behavioral Finance -- 1. Introduction -- 2. A model for assets and liabilities -- 3. Expected utility framework -- 3.1. The optimization problem -- 4. Extension to cumulative prospect theory -- 4.1. The optimization problem -- 4.2. Probability distortion function -- 5. Comparison -- 5.1. Partial surplus optimization -- 5.2. Connection between CPT optimization, funding ratio optimization and partial surplus optimization -- 6. Conclusion -- Acknowledgment -- Appendix A. Solution of the HJB equation -- Appendix B. Quantile optimization approach -- Appendix C. Probability distortion -- Appendix D. Replicating strategies for selected pay-offs -- Bibliography -- 12. Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model -- 1. Introduction -- 2. Regime-switching autoregressive models -- 2.1. Regime prediction -- 2.1.1. Filtering algorithm -- 2.1.2. Conditional distribution -- 2.1.3. Stationary distribution in the Gaussian case -- 2.2. Estimation of parameters -- 2.3. Goodness-of-fit test and selection of the number of regimes -- 2.4. Application to S& -- P 500 daily returns -- 3. Optimal discrete time hedging -- 3.1. Implementation issues -- 3.1.1. Using regime predictions -- 3.2. Optimal hedging vs delta-hedging -- 3.3. Simulated hedging errors -- 4. Out-of-sample vanilla pricing and hedging -- 4.1. Methodology -- 4.1.1. The underlying asset. , 4.1.2. Option dataset -- 4.1.3. Backtesting -- 4.2. Empirical results -- 4.2.1. 2008-2009 Financial Crisis -- 4.2.2. 2013-2015 Bull markets -- 5. Conclusion -- Appendix A. Extension of Baum-Welch algorithm -- Appendix A.1. Estimation of regime-switching models -- Appendix B. Goodness-of-fit test for ARHMM -- Appendix B.1. Rosenblatt's transform -- Appendix B.2. Test statistic -- Appendix B.3. Parametric bootstrap algorithm -- References -- 13. Interest Rate Swap Valuation in the Chinese Market -- 1. Introduction -- 2. Pricing model -- 2.1. Dual curve discounting -- 2.2. Single curve discounting -- 2.3. Valuation difference -- 3. Candidates for the risk-free rate in the Chinese swap market -- 4. Numerical test -- 5. Conclusion -- References -- 14. On Consistency of the Omega Ratio with Stochastic Dominance Rules -- 1. Introduction -- 2. Omega ratios and stochastic dominance -- 3. Omega ratios and combined concave and convex stochastic dominance -- References -- 15. Chance-Risk Classification of Pension Products: Scientific Concepts and Challenges -- 1. Introduction -- 2. Typical private pension products offered in Germany -- 3. Aspects of chance-risk classification concepts -- 4. Capital market model and simulation of important product ingredients -- 5. Scientific challenges and outlook -- References -- 16. Forward versus Spot Price Modeling -- 1. Introduction -- 2. Spot and forward model -- 2.1. Spot model -- 2.2. Forward model -- 2.2.1. Wealth process model -- 3. First example: CEV model -- 4. Second example: JDCEV model -- 5. Implications for modeling -- 6. Conclusion -- Appendix A. Martingale property of driving process -- Appendix B. Density of ST in JDCEV model -- References -- 17. Replication Methods for Financial Indexes -- 1. Introduction -- 2. Replication methods -- 2.1. Factorial approach for strong replication -- 2.2. Weak replication. , 2.2.1. Implementation steps. , English

Language: English

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Format: 1 online resource (434 pages)

ISBN: 9783319091143

Series Statement: Springer Proceedings in Mathematics and Statistics Ser. ; v.99

Note: Intro -- Preface I -- Preface II -- Contents -- Part I Markets, Regulation,and Model Risk -- A Random Holding Period Approach for Liquidity-Inclusive Risk Management -- 1 Introduction -- 1.1 Earlier Literature -- 1.2 Different Risk Horizons Are Acknowledged by BCBS -- 2 The Univariate Case -- 2.1 A Brief Review on the Stochastic Holding Period Framework -- 2.2 Semi-analytic Solutions and Simulations -- 3 Dependence Modeling: A Bivariate Case -- 4 Calibration with Liquidity Data -- 4.1 Dependencies Between Liquidity, Credit, and Market Risk -- 4.2 Marginal Distributions of SHPs -- 5 Conclusions -- References -- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models -- 1 Introduction -- 2 Loss of Confidence in Internal Models---How Did It Happen? -- 2.1 An Example from the First Years of the Crisis -- 2.2 Divergence of Model Results -- 3 Alternatives to Internal Models -- 3.1 Overview -- 3.2 The Leverage Ratio -- 3.3 Regulatory Standardised Approaches -- 4 Ways of Restoring Confidence -- 4.1 Overview -- 4.2 Reducing the Variation in Model Results Through Standardisation -- 4.3 Enhancing Transparency -- 4.4 Highlighting the Positive Developments as a Result of the Trading Book Review -- 4.5 Strengthening the Use Test Concept -- 4.6 A Comprehensive Approach to Model Validation -- 4.7 Quantification and Capitalisation of Model Risk -- 4.8 Voluntary Commitment by Banks to a Code of ``Model Ethics'' -- 4.9 Other Approaches -- 5 Conclusion -- References -- Model Risk in Incomplete Markets with Jumps -- 1 Introduction -- 2 Losses from Hedged Positions -- 2.1 Market and Model Setup -- 2.2 Loss Process -- 2.3 Loss Distribution -- 3 Measures of Model Risk -- 3.1 Value-at-Risk and Expected Shortfall -- 3.2 Axioms for Measures of Model Risk -- 4 Hedge Differences -- 5 Application to Energy Markets -- References. , Part II Financial Engineering -- Bid-Ask Spread for Exotic Options under Conic Finance -- 1 Introduction -- 2 Exotic Bid-Ask Spread -- 3 Conclusion -- References -- Derivative Pricing under the Possibility of Long Memory in the supOU Stochastic Volatility Model -- 1 Introduction -- 2 A Review of the supOU Stochastic Volatility Model -- 3 Martingale Conditions -- 4 Fourier Pricing in the supOU Stochastic Volatility Model -- 4.1 A Review on Fourier Pricing -- 4.2 The Characteristic Function -- 4.3 Regularity of the Moment Generating Function -- 5 Examples -- 5.1 Concrete Specifications -- 5.2 Calibration and an Illustrative Example -- References -- A Two-Sided BNS Model for Multicurrency FX Markets -- 1 Introduction -- 2 The Two-Sided Barndorff--Nielsen--Shephard Model Class -- 3 A Tractable Multivariate Extension of the Two-Sided Γ-OU-BNS Model -- 4 Modeling Two FX Rates with a Bivariate Two-Sided Γ-OU-BNS Model -- 4.1 The Dependence Structure of the Lévy Drivers -- 4.2 Implicitly Defined Models -- 5 Application: Calibration to FX Rates and Pricing of Bivariate FX Derivatives -- 5.1 Data -- 5.2 Model Setup -- 5.3 Calibration -- 6 Conclusion and Outlook -- References -- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors -- 1 Introduction -- 2 A Review of the Model by Stoll and Wiebauer (2010) -- 3 The Oil Price Dependence of Gas Prices -- 4 Model Calibration with Temperature and Oil Price -- 4.1 Oil Price Model -- 4.2 Temperature Model -- 4.3 The Residual Stochastic Process -- 5 Option Valuation by Least Squares Monte Carlo Including Exogenous Components -- 5.1 Extensions of Least Squares Monte Carlo Algorithm Including Exogenous Components -- 5.2 Influence of Exogenous Components on Valuation Results -- 6 Conclusion -- References -- Copula-Specific Credit Portfolio Modeling -- 1 Introduction. , 2 Copulas Under Consideration -- 3 A Comparison Between CreditRisk+ and CreditMetrics -- 3.1 Preliminary Notes and General Remarks -- 3.2 Theoretical Background -- 4 Results on Estimated Copulas and Risk Figures -- 4.1 Portfolio and Model Calibration -- 4.2 Parametrization of Marginal Distributions -- 4.3 Estimation of Copulas -- 4.4 Effect of the Copula on the Risk Figures and the Tail of the Loss Distribution -- 5 Summary -- References -- Implied Recovery Rates---Auctions and Models -- 1 Introduction -- 2 CDS Settlement: Credit Auction -- 2.1 Initial Biding Period -- 2.2 Dutch Auction -- 2.3 Summary of the Auction Procedure -- 3 Examples of Implied Recovery Models -- 3.1 Cox--Ingersoll--Ross Type Reduced-Form Model -- 3.2 Pure Recovery Model -- 4 Conclusion and Outlook -- References -- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence -- 1 Currency Carry Trade and Uncovered Interest Rate Parity -- 2 Interpreting Tail Dependence as Financial Risk Exposure in Carry Trade Portfolios -- 3 Generalised Archimedean Copula Models for Currency Exchange Rate Baskets -- 4 Currency Basket Model Estimations via Inference Function for the Margins -- 4.1 Stage 1: Fitting the Marginal Distributions via MLE -- 4.2 Stage 2: Fitting the Mixture Copula via MLE -- 5 Exchange Rate Multivariate Data Description and Currency Portfolio Construction -- 6 Results and Discussion -- 6.1 Tail Dependence Results -- 6.2 Pairwise Decomposition of Basket Tail Dependence -- 6.3 Understanding the Tail Exposure Associated with the Carry Trade and Its Role in the UIP Puzzle -- 7 Conclusion -- References -- Part III Insurance Riskand Asset Management -- Participating Life Insurance Contracts under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design -- 1 Introduction -- 2 Considered Products. , 2.1 The Traditional Product -- 2.2 Alternative Products -- 3 Stochastic Modeling and Analyzed Key Figures -- 3.1 The Financial Market Model -- 3.2 The Asset-Liability Model -- 3.3 Key Drivers for Capital Efficiency -- 4 Results -- 4.1 Assumptions -- 4.2 Comparison of Product Designs -- 4.3 Sensitivity Analyses -- 4.4 Reduction in the Level of Guarantee -- 5 Conclusion and Outlook -- References -- Reducing Surrender Incentives Through Fee Structure in Variable Annuities -- 1 Introduction -- 2 Assumptions and Model -- 2.1 Variable Annuity -- 2.2 Benefits -- 3 Valuation of the Surrender Option -- 3.1 Notation and Optimal Surrender Decision -- 3.2 Theoretical Result on Optimal Surrender Behavior -- 3.3 Valuation of the Surrender Option Using PDEs -- 4 Numerical Example -- 4.1 Numerical Results -- 5 Concluding Remarks -- References -- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment -- 1 Introduction -- 2 The Mean-Variance-Optimal Deterministic Consumption and Investment Problem -- 3 Existence of Optimal Deterministic Control Functions -- 4 A Pontryagin Maximum Principle -- 5 Generalized Gradients for the Objective -- 6 Numerical Optimization by a Gradient Ascent Method -- 7 Numerical Example -- References -- Risk Control in Asset Management: Motives and Concepts -- 1 Introduction -- 2 Risk Management for Active Portfolios -- 2.1 Factor Structure and Portfolio Risk -- 2.2 Allocation to Active and Passive Funds -- 3 Dealing with Investors Downside-Risk Aversion -- 3.1 Portfolio Insurance -- 3.2 Popular Portfolio Insurance Strategies -- 3.3 Performance Comparison -- 3.4 Other Risks -- 4 Parameter Uncertainty and Model Uncertainty -- 4.1 Parameter Uncertainty -- 4.2 Model Uncertainty -- 5 Conclusion -- References -- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash -- 1 Introduction. , 1.1 Alternative Ansatz of Korn and Wilmott -- 1.2 Literature Review -- 2 Setup of the Model -- 3 Optimal Portfolios Given the Probability of a Crash -- 4 The q-quantile Crash Hedging Strategy -- 5 Examples -- 5.1 Uniformly Distributed Crash Sizes -- 5.2 Conditional Exponential Distributed Crash Sizes -- 5.3 Conditional Exponential Distributed Crash Sizes with Exponential Distributed Crash Times -- 6 Deterministic Portfolio Strategies -- 7 Conclusion -- References -- Improving Optimal Terminal Value Replicating Portfolios -- 1 Introduction -- 2 The Mathematical Setup -- 3 The Theory of Replicating Portfolios -- 3.1 Cash-Flow Matching -- 3.2 Discounted Terminal Value Matching -- 4 Equivalence of Cash-Flow Matching and Discounted Terminal Value Matching -- 5 Example -- 6 Conclusion -- References -- Part IV Computational Methodsfor Risk Management -- Risk and Computation -- 1 Computational Risk -- 1.1 Efficiency of Algorithms -- 1.2 Risk of an Algorithm -- 1.3 Eliminate the Risk -- 1.4 Effort -- 1.5 Example -- 2 Assessing Structural Risk -- 2.1 Simplest Attractor -- 2.2 Mean-Field Models -- 2.3 Artificial Example -- 2.4 Structure in Phase Spaces -- 2.5 Risk Index -- 2.6 Example -- 2.7 Summary -- References -- Extreme Value Importance Sampling for Rare Event Risk Measurement -- 1 Introduction -- 2 The One-Dimensional Case -- 3 Examples -- 3.1 Example 1: Simulation Estimators of Quantiles and TailVar for the Normal Distribution -- 3.2 Example 2: Simulating a Portfolio Credit Risk Model -- 4 Conclusion -- References -- A Note on the Numerical Evaluation of the Hartman--Watson Density and Distribution Function -- 1 Introduction -- 2 Occurrence of the Hartman--Watson Law -- 3 Straightforward Implementation Based on Formula (1) -- 4 Evaluation via Gaver--Stehfest Laplace Inversion. , 5 Evaluation via a Complex Laplace Inversion Method for the Bondesson Class.

Additional Edition: Print version: Glau, Kathrin Innovations in Quantitative Risk Management Cham : Springer International Publishing AG,c2015 ISBN 9783319091136

Language: English

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Format: 1 online resource (X, 449 p. 68 illus., 43 illus. in color.)

Edition: 1st ed. 2016.

ISBN: 3-319-33446-8

Series Statement: Springer Proceedings in Mathematics & Statistics, 165

Content: This book presents 20 peer-reviewed chapters on current aspects of derivatives markets and derivative pricing. The contributions, written by leading researchers in the field as well as experienced authors from the financial industry, present the state of the art in: • Modeling counterparty credit risk: credit valuation adjustment, debit valuation adjustment, funding valuation adjustment, and wrong way risk. • Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling. • Recent developments concerning contingent convertible bonds, the measuring of basis spreads, and the modeling of implied correlations. The recent financial crisis has cast tremendous doubts on the classical view on derivative pricing. Now, counterparty credit risk and liquidity issues are integral aspects of a prudent valuation procedure and the reference interest rates are represented by a multitude of curves according to their different periods and maturities. A panel discussion included in the book (featuring Damiano Brigo, Christian Fries, John Hull, and Daniel Sommer) on the foundations of modeling and pricing in the presence of counterparty credit risk provides intriguing insights on the debate. .

Note: Foreword -- Preface -- Part I: Valuation Adjustments -- Part II: Fixed Income Modeling -- Part III: Financial Engineering. .

Additional Edition: ISBN 3-319-33445-X

Language: English

DOI: 10.1007/978-3-319-33446-2

UID:

Format: 1 online resource (446 pages)

ISBN: 9783319334462

Series Statement: Springer Proceedings in Mathematics and Statistics Ser. ; v.165

Note: Intro -- Preface -- Foreword -- Contents -- Part I Valuation Adjustments -- Nonlinearity Valuation Adjustment -- 1 Introduction -- 2 Trading Under Collateralization, Close-Out Netting, and Funding Risk -- 2.1 Collateralization -- 2.2 Close-Out Netting -- 2.3 Funding Risk -- 3 Generalized Derivatives Valuation -- 3.1 Discrete-Time Solution -- 3.2 Continuous-Time Solution -- 4 Nonlinear Valuation: A Numerical Analysis -- 4.1 Monte Carlo Pricing -- 4.2 Case Outline -- 4.3 Preliminary Valuation Under Symmetric Funding and Without Credit Risk -- 4.4 Complete Valuation Under Credit Risk, Collateral, and Asymmetric Funding -- 4.5 Nonlinearity Valuation Adjustment -- 5 Conclusions and Financial Implications -- References -- Analysis of Nonlinear Valuation Equations Under Credit and Funding Effects -- 1 Introduction -- 2 Cash Flows Analysis and First Valuation Equation -- 2.1 The Cash Flows -- 2.2 Adjusted Cash Flows Under a Simple Trading Model -- 3 An FBSDE Under mathcalF -- 4 Markovian FBSDE and PDE for widetildeVt and the Invariance Theorem -- References -- Nonlinear Monte Carlo Schemes for Counterparty Risk on Credit Derivatives -- 1 Introduction -- 2 Prices -- 2.1 Setup -- 2.2 Clean Price -- 2.3 All-Inclusive Price -- 3 TVA BSDEs -- 3.1 Full TVA BSDE -- 3.2 Partially Reduced TVA BSDE -- 3.3 Fully Reduced TVA BSDE -- 3.4 Marked Default Time Setup -- 4 TVA Numerical Schemes -- 4.1 Linear Approximation -- 4.2 Linear Expansion and Interacting Particle Implementation -- 4.3 Marked Branching Diffusion Approach -- 5 TVA Models for Credit Derivatives -- 5.1 Dynamic Gaussian Copula TVA Model -- 5.2 Dynamic Marshall--Olkin Copula TVA Model -- 5.3 Strong Versus Weak Dynamic Copula Model -- 6 Numerics -- 6.1 Numerical Results in the DGC Model -- 6.2 Numerical Results in the DMO Model -- 7 Conclusion -- References. , Tight Semi-model-free Bounds on (Bilateral) CVA -- 1 Introduction -- 2 Counterparty Default Risk -- 3 The Main Building Blocks of CVA -- 4 Models for Counterparty Risk -- 4.1 Independence of CVA Components -- 4.2 Modeling Options on the Basis Transaction -- 4.3 Hybrid Models---An Example -- 5 Tight Bounds on CVA -- 5.1 Tight Bounds on CVA by Mass Transportation -- 5.2 An Alternative Formulation as Assignment Problem -- 6 Example -- 6.1 Setup -- 6.2 Results -- 6.3 Computation Time, Choice of Algorithm, and Impact of Assumptions -- 7 Conclusion and Outlook -- References -- CVA with Wrong-Way Risk in the Presence of Early Exercise -- 1 Introduction -- 2 CVA Pricing and WWR -- 3 The Impact of Early Exercise -- 3.1 The Pricing Problem -- 3.2 The Plain Vanilla Case -- 4 The Bermudan Swaption Case -- 5 Concluding Remarks -- References -- Simultaneous Hedging of Regulatory and Accounting CVA -- 1 Introduction -- 2 Counterparty Risk from a Regulatory Perspective: The Standardized CVA Risk Charge -- 2.1 Standardized CVA Risk Charge as Volatility -- 3 Counterparty Risk from an Accounting Perspective -- 3.1 CVA Hedging from an Accounting Perspective -- 4 Portfolio P& -- L -- 4.1 Portfolio P& -- L Without CVA -- 4.2 Impact with CVA -- 4.3 Impact of CVA Risk Charge Hedging on the Accounting P& -- L Volatility -- 5 Determination of the Optimal Hedge Strategy -- 5.1 Special Cases -- References -- Capital Optimization Through an Innovative CVA Hedge -- 1 Preface -- 2 The Role of Collateral in OTC Contracts and Its Legal Basis -- 2.1 The Role of Legal Versus Economic Ownership -- 2.2 Affected Market Participants -- 2.3 Financial Instruments Involving Collateral and Standard Legal Frameworks (Master Agreements) -- 2.4 Credit and Counterparty Risk Related to Collateral -- 3 Terms of Liquidity and Definition of Liquidity Transformation. , 3.1 Terms of Liquidity -- 3.2 Comparison of Secured and Unsecured Financing -- 3.3 Liquidity Transformation -- 4 New Approach to CVA Hedging -- 4.1 Issue -- 4.2 Solution -- 4.3 Application -- 4.4 Example -- 5 Conclusion -- References -- FVA and Electricity Bill Valuation Adjustment---Much of a Difference? -- 1 Welcome -- 2 Damiano Brigo -- 3 Christian Fries -- 4 John Hull -- 5 Daniel Sommer -- 5.1 Acknowledgements, Credits, and Disclaimer -- References -- Part II Fixed Income Modeling -- Multi-curve Modelling Using Trees -- 1 Introduction -- 2 The LIBOR-OIS Spread -- 3 The Methodology -- 4 A Simple Three-Step Example -- 5 Valuation of a Spread Option -- 6 Bermudan Swap Option -- 7 Conclusions -- References -- Derivative Pricing for a Multi-curve Extension of the Gaussian, Exponentially Quadratic Short Rate Model -- 1 Introduction -- 2 Preliminaries -- 2.1 Discount Curve and Collateralization -- 2.2 Martingale Measures -- 3 Short Rate Model -- 3.1 The Model -- 3.2 Bond Prices (OIS and Libor Bonds) -- 3.3 Forward Measure -- 4 Pricing of Linear Interest Rate Derivatives -- 4.1 FRAs -- 4.2 Interest Rate Swaps -- 5 Nonlinear/optional Interest Rate Derivatives -- 5.1 Caps and Floors -- 5.2 Swaptions -- References -- Multi-curve Construction -- 1 Introduction -- 2 Foundations, Assumptions, Notation -- 3 Discount Curves -- 4 Forward Curves -- 4.1 Performance Index of a Discount Curve (or ``Self-Discounting'') -- 5 Interpolation of Curves -- 5.1 Implementing the Interpolation of a Curve: Interpolation Method and Interpolation Entities -- 5.2 Interpolation Time -- 5.3 Interpolation of Forward Curves -- 5.4 Assessment of the Interpolation Method -- 6 Implementation of the Calibration of Curves -- 6.1 Generalized Definition of a Swap -- 6.2 Calibration of Discount Curve to Swap Paying the Collateral Rate (aka. Self-Discounted Swaps). , 6.3 Calibration of Forward Curves -- 6.4 Calibration of Discount Curves When Payment and Collateral Currency Differ -- 6.5 Lack of Calibration Instruments (for Difference in Collateralization) -- 6.6 Implementation -- 7 Redefining Forward Rate Market Models -- 8 Some Numerical Results -- 8.1 Impact of the Interpolation Entity of a Forward Curve on the Delta Hedge -- 8.2 Impact of the Lack of Calibration Instruments for the Case of a Foreign Swap Collateralized in Domestic Currency -- 8.3 Impact of the Interpolation Scheme on the Hedge Efficiency -- 9 Conclusion -- References -- Impact of Multiple-Curve Dynamics in Credit Valuation Adjustments -- 1 Introduction -- 2 Valuation Equation with Credit and Collateral -- 2.1 Valuation Framework -- 2.2 The Master Equation Under Change of Filtration -- 3 Valuing Collateralized Interest-Rate Derivatives -- 3.1 Overnight Rates and OIS -- 3.2 LIBOR Rates, IRS and Basis Swaps -- 3.3 Modeling Constraints -- 4 Interest-Rate Modeling -- 4.1 Multiple-Curve Collateralized HJM Framework -- 4.2 Numerical Results -- References -- A Generalized Intensity-Based Framework for Single-Name Credit Risk -- 1 Introduction -- 2 A General Account on Credit Risky Bond Markets -- 2.1 The Generalized Intensity-Based Framework -- 2.2 An Extension of the HJM Approach -- 3 Affine Models in the Generalized Intensity-Based Framework -- 4 Conclusion -- References -- Option Pricing and Sensitivity Analysis in the Lévy Forward Process Model -- 1 Introduction -- 2 The Lévy Forward Process Model -- 3 Fourier-Based Methods for Option Pricing -- 4 Sensitivity Analysis -- 4.1 Greeks Computed by the Malliavin Approach -- 4.2 Greeks Computed by the Fourier-Based Valuation Method -- 4.3 Examples -- References -- Inside the EMs Risky Spreads and CDS-Sovereign Bonds Basis -- 1 Introduction -- 2 Local Currency Bonds No-Arbitrage HJM Setting. , 2.1 Risky Bonds Under Marked Point Process -- 2.2 Model Formulation -- 3 CDS-Bond Basis -- 3.1 General Notes -- 3.2 Technical Notes -- 3.3 CDS-Bond Basis Empirics -- 4 Conclusion -- References -- Part III Financial Engineering -- Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model -- 1 Introduction -- 2 The One-Factor Lévy Model -- 2.1 The Model -- 2.2 The Risk-Neutral Stock Price Processes -- 3 A Three-Moments-Matching Approximation -- 3.1 Matching the First Three Moments -- 3.2 Approximate Basket Option Pricing -- 3.3 The FFT Method and Basket Option Pricing -- 4 Examples and Numerical Illustrations -- 4.1 Variance Gamma -- 4.2 Pricing Basket Options -- 5 Implied Lévy Correlation -- 5.1 Variance Gamma -- 5.2 Double Exponential -- 6 Conclusion -- References -- Pricing Shared-Loss Hedge Fund Fee Structures -- 1 Introduction -- 2 Hedge Fund Fees -- 3 The First-Loss Model -- 4 An Option Pricing Framework -- 4.1 Payoff to the Investor -- 4.2 Payoff to the Manager -- 4.3 Valuation: Pricing Fees as Derivatives -- 5 Consequences of the Derivative Pricing Framework -- 5.1 Graphical Analysis -- 5.2 Sensitivity Analysis -- 6 Conclusion -- References -- Negative Basis Measurement: Finding the Holy Scale -- 1 Introduction -- 2 Why Does Negative Basis Exist? -- 3 General Notations -- 4 Traditional Measurements -- 4.1 The Z-Spread Methodology -- 4.2 The Par-Equivalent CDS Methodology -- 5 An Innovative Methodology -- 6 Conclusion -- References -- The Impact of a New CoCo Issuance on the Price Performance of Outstanding CoCos -- 1 Introduction -- 2 The Equity Derivatives Model -- 3 Measuring the Price Performance of the Outstanding CoCos -- 3.1 New Issuances -- 3.2 CoCo Index Comparison -- 3.3 Model-Based Performance -- 4 Impact After Issue Date -- 5 Conclusion -- References -- The Impact of Cointegration on Commodity Spread Options. , 1 Introduction.

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Format: 1 online resource (xi, 438 pages) : , illustrations; digital, PDF file(s).

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Series Statement: Springer Proceedings in Mathematics & Statistics, 99

Content: Quantitative models are omnipresent –but often controversially discussed– in todays risk management practice. New regulations, innovative financial products, and advances in valuation techniques provide a continuous flow of challenging problems for financial engineers and risk managers alike. Designing a sound stochastic model requires finding a careful balance between parsimonious model assumptions, mathematical viability, and interpretability of the output. Moreover, data requirements and the end-user training are to be considered as well. The KPMG Center of Excellence in Risk Management conference Risk Management Reloaded and this proceedings volume contribute to bridging the gap between academia –providing methodological advances– and practice –having a firm understanding of the economic conditions in which a given model is used. Discussed fields of application range from asset management, credit risk, and energy to risk management issues in insurance. Methodologically, dependence modeling, multiple-curve interest rate-models, and model risk are addressed. Finally, regulatory developments and possible limits of mathematical modeling are discussed.

Note: Bibliographic Level Mode of Issuance: Monograph , Part I Markets, Regulation, and Model Risk -- A Random Holding Period Approach for Liquidity-Inclusive Risk Management -- Regulatory Developments in Risk Management: Restoring Confidence in Internal Models -- Model Risk in Incomplete Markets with Jumps -- Part II Financial Engineering -- Bid-Ask Spread for Exotic Options Under Conic Finance -- Derivative Pricing Under the Possibility of Long Memory in the supOU Stochastic Volatility Model -- A Two-Sided BNS Model for Multicurrency FX Markets -- Modeling the Price of Natural Gas with Temperature and Oil Price as Exogenous Factors -- Copula-Specific Credit Portfolio Modeling -- Implied Recovery Rates—Auctions and Models -- Upside and Downside Risk Exposures of Currency Carry Trades via Tail Dependence -- Part III Insurance Risk and Asset Management -- Participating Life Insurance Contracts Under Risk Based Solvency Frameworks: How to Increase Capital Efficiency by Product Design -- Reducing Surrender Incentives Through Fee Structure in Variable Annuities -- A Variational Approach for Mean-Variance-Optimal Deterministic Consumption and Investment -- Risk Control in Asset Management: Motives and Concepts -- Worst-Case Scenario Portfolio Optimization Given the Probability of a Crash -- Improving Optimal Terminal Value Replicating Portfolios -- Part IV Computational Methods for Risk Management -- Risk and Computation -- Extreme Value Importance Sampling for Rare Event Risk Measurement -- A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function -- Computation of Copulas by Fourier Methods -- Part V Dependence Modelling -- Goodness-of-fit Tests for Archimedean Copulas in High Dimensions -- Duality in Risk Aggregation -- Some Consequences of the Markov Kernel Perspective of Copulas -- Copula Representations for Invariant Dependence Functions -- Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection. , Also available in print form. , English

Additional Edition: Print version: ISBN 9783319091136

Language: English

DOI: 10.1007/978-3-319-09114-3