Provides valuable, practical information about credit risks, exotic/hybrid options, retirement plans/pensions, life insurance, portfolio selection, incentive schemes, and interest rate modeling

Presents a variety of novel mathematical methods involving finite-difference, Monte Carlo, and fast Fourier transform techniques

Offers realistic alternatives to the VaR approach used in financial risk management practice

Identifies potential pitfalls of standard methodologies

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 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