Numerical Methods for Finance

Numerical Methods for Finance

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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 more

Product details

  • Hardback | 312 pages
  • 162.56 x 238.76 x 22.86mm | 566.99g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 59 black & white illustrations, 63 black & white tables
  • 158488925X
  • 9781584889250

Table of contents

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 INDEXshow more

About John Miller

Institute for Numerical Computation & Analysis, Dublin, Irel University College Dublin, Co. Dublin, Ireland Dublin City University, Irelandshow more