Statistical Validation of Partial Differential Equation Solvers in Finance: Using Logistic Regression to Quantify Risk of Numerical Pricing Error
Abstract
This study investigates the stability and accuracy of the Crank-Nicolson finite difference method for pricing European put options under the Black-Scholes model in weighted Sobolev spaces. An a priori error estimate is derived showing unconditional stability and error of order ( ) ( ) 2 2 2 0 . h + Numerical experiments with 400, 200 M N = = and Rannacher smoothing confirm that relative error increases monotonically with volatility, from 0.016% at 0.25 = to
Keywords
Black-Scholes PDECrank-Nicolson methodWeighted Sobolev spaceVolatilityDerivatives pricingLogistic regression and Numerical analysis.
References
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