Numerical Methods for Finance

Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is one of the few books entirely devoted to numerical methods as applied to the financial field.Presenting state-of-the-art methods in this area, the book first discusses the coherent risk measures theory and how it applies to practical risk management. It then proposes a new method for pricing high-dimensional American options, followed by a description of the negative inter-risk diversification effects between credit and market risk. After evaluating counterparty risk for interest rate payoffs, the text considers strategies and issues concerning defined contribution pension plans and participating life insurance contracts. It also develops a computationally efficient swaption pricing technology, extracts the underlying asset price distribution implied by option prices, and proposes a hybrid GARCH model as well as a new affine point process framework. In addition, the book examines performance-dependent options, variance reduction, Value at Risk (VaR), the differential evolution optimizer, and put-call-futures parity arbitrage opportunities.Sponsored by DEPFA Bank, IDA Ireland, and Pioneer Investments, this concise and well-illustrated book equips practitioners with the necessary information to make important financial decisions.

COHERENT MEASURES OF RISK INTO EVERYDAY MARKET PRACTICEMotivationsCoherency Axioms and the Shortcomings of VaR The Objectivist Paradigm Estimability The Diversification Principle RevisitedSpectral Measures of Risk Estimators of Spectral Measures Optimization of CRMs: Exploiting ConvexityConclusions PRICING HIGH-DIMENSIONAL AMERICAN OPTIONS USING LOCAL CONSISTENCY CONDITIONSIntroduction FormulationOutline of the Method Stability AnalysisBoundary Points ExperimentsConclusionsADVERSE INTER-RISK DIVERSIFICATION EFFECTS FOR FX FORWARDSIntroduction Related ResearchThe ModelPortfolio and DataResultsConclusionsCOUNTERPARTY RISK UNDER CORRELATION BETWEEN DEFAULT AND INTEREST RATESIntroduction General Valuation of Counterparty RiskModeling AssumptionsNumerical MethodsResults and DiscussionResults Interpretation and ConclusionsOPTIMAL DYNAMIC ASSET ALLOCATION FOR DEFINED CONTRIBUTION PENSION PLANSSummary of Cairns, Blake, and DowdON HIGH-PERFORMANCE SOFTWARE DEVELOPMENT FOR THE NUMERICAL SIMULATION OF LIFE INSURANCE POLICIESIntroductionComputational Kernels in Participating Life Insurance PoliciesNumerical Methods for the Computational KernelsA Benchmark Mathematical Model Numerical Experiments Conclusions References AN EFFICIENT NUMERICAL METHOD FOR PRICING INTEREST RATE SWAPTIONSIntroduction Pricing Swaptions Using Integral TransformsPricing Swaptions Using the FFTApplication and Computational AnalysisModel Testing Using EURIBOR Swaptions DataConclusions and Future ResearchEMPIRICAL TESTING OF LOCAL CROSS ENTROPY AS A METHOD FOR RECOVERING ASSET'S RISK-NEUTRAL PDF FROM OPTION PRICESIntroductionMethodologyResultsConclusionUSING INTRADAY DATA TO FORECAST DAILY VOLATILITY: A HYBRID APPROACHIntroduction The Hybrid Framework Adding Intraday Data to the FrameworkConclusion PRICING CREDIT FROM THE TOP DOWN WITH AFFINE POINT PROCESSES Extended AbstractVALUATION OF PERFORMANCE-DEPENDENT OPTIONS IN A BLACK-SCHOLES FRAMEWORKIntroduction Performance-Dependent OptionsNumerical ResultsVARIANCE REDUCTION THROUGH MULTILEVEL MONTE CARLO PATH CALCULATIONSIntroductionMultilevel Monte Carlo Method Numerical ResultsConcluding Remarks VALUE AT RISK AND SELF-SIMILARITYIntroduction The Set Up Risk Estimation for Different Hurst Coefficients Estimating Hurst ExponentsUsed Techniques Estimating the Scaling LawDetermining the Hurst Exponent InterpretationConclusion and OutlookAcknowledgmentPARAMETER UNCERTAINTY IN KALMAN FILTER ESTIMATION OF THE CIR TERM STRUCTURE MODELIntroductionDynamic Term Structure ModelsDifferential Evolution ResultsConclusionEDDIE FOR DISCOVERING ARBITRAGE OPPORTUNITIESINDEX