Numerical Methods for Finance

Abstract

COHERENT MEASURES OF RISK INTO EVERYDAY MARKET PRACTICE Motivations Coherency Axioms and the Shortcomings of VaR The Objectivist Paradigm Estimability The Diversification Principle Revisited Spectral Measures of Risk Estimators of Spectral Measures Optimization of CRMs: Exploiting Convexity Conclusions PRICING HIGH-DIMENSIONAL AMERICAN OPTIONS USING LOCAL CONSISTENCY CONDITIONS Introduction Formulation Outline of the Method Stability Analysis Boundary Points Experiments Conclusions ADVERSE INTER-RISK DIVERSIFICATION EFFECTS FOR FX FORWARDS Introduction Related Research The Model Portfolio and Data Results Conclusions COUNTERPARTY RISK UNDER CORRELATION BETWEEN DEFAULT AND INTEREST RATES Introduction General Valuation of Counterparty Risk Modeling Assumptions Numerical Methods Results and Discussion Results Interpretation and Conclusions OPTIMAL DYNAMIC ASSET ALLOCATION FOR DEFINED CONTRIBUTION PENSION PLANS Summary of Cairns, Blake, and Dowd ON HIGH-PERFORMANCE SOFTWARE DEVELOPMENT FOR THE NUMERICAL SIMULATION OF LIFE INSURANCE POLICIES Introduction Computational Kernels in Participating Life Insurance Policies Numerical Methods for the Computational Kernels A Benchmark Mathematical Model Numerical Experiments Conclusions References AN EFFICIENT NUMERICAL METHOD FOR PRICING INTEREST RATE SWAPTIONS Introduction Pricing Swaptions Using Integral Transforms Pricing Swaptions Using the FFT Application and Computational Analysis Model Testing Using EURIBOR Swaptions Data Conclusions and Future Research EMPIRICAL TESTING OF LOCAL CROSS ENTROPY AS A METHOD FOR RECOVERING ASSET'S RISK-NEUTRAL PDF FROM OPTION PRICES Introduction Methodology Results Conclusion USING INTRADAY DATA TO FORECAST DAILY VOLATILITY: A HYBRID APPROACH Introduction The Hybrid Framework Adding Intraday Data to the Framework Conclusion PRICING CREDIT FROM THE TOP DOWN WITH AFFINE POINT PROCESSES Extended Abstract VALUATION OF PERFORMANCE-DEPENDENT OPTIONS IN A BLACK-SCHOLES FRAMEWORK Introduction Performance-Dependent Options Numerical Results VARIANCE REDUCTION THROUGH MULTILEVEL MONTE CARLO PATH CALCULATIONS Introduction Multilevel Monte Carlo Method Numerical Results Concluding Remarks VALUE AT RISK AND SELF-SIMILARITY Introduction The Set Up Risk Estimation for Different Hurst Coefficients Estimating Hurst Exponents Used Techniques Estimating the Scaling Law Determining the Hurst Exponent Interpretation Conclusion and Outlook Acknowledgment PARAMETER UNCERTAINTY IN KALMAN FILTER ESTIMATION OF THE CIR TERM STRUCTURE MODEL Introduction Dynamic Term Structure Models Differential Evolution Results Conclusion EDDIE FOR DISCOVERING ARBITRAGE OPPORTUNITIES INDEX

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