Numerical Methods for Finance
John Miller, David Edelman, John Appleby
CRC Press, Sep 21, 2007 - Mathematics - 312 pages
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.
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1FCIR 1FGV 24 DAX stocks 2FGV 2FV model affine algorithm American options asset benchmark Bermudan Black–Scholes bond prices Brigo Brownian motion Carlo Methods Cauchy distribution chapter CIR model computational condition consider convergence correlation counterparty risk credit risk CRMs defined derivatives detrended dimension discretization dynamics equation error curves evaluation factor FFT-SP Figure financial time series forecast function given Glasserman grid points Hurst coefficient Hurst exponent implied volatility interest rates interest-rate intraday Journal Kalman filter KF GARCH linear log-likelihood martingale Mathematics matrix mean MLCE Monte Carlo method Monte Carlo simulation normal distribution one-factor optimal parameter vectors option prices out-of-sample parameter estimates payoff Pelsser 21 portfolio problem Put Options quantile regression riskless sample scaling law Schrager and Pelsser SDEs self-similar short rate solution standard stochastic volatility strike price swap swaption contracts swaption pricing methodology TABLE term-structure models underlying variables variance Vasicek models zero
Page ii - Portfolio Optimization and Performance Analysis, Jean-Luc Prigent Robust Libor Modelling and Pricing of Derivative Products, John Schoenmakers Structured Credit Portfolio Analysis, Baskets & CDOs, Christian Bluhm and Ludger Overbeck Numerical Methods for Finance, John AD Appleby, David C.