Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
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The integrands in M. Schröder’s integral representation for the price of Asian options are highly oscillatory yielding cancellations of many digits in the integration. Furthermore, obtaining multiple precision function values is costly. Numerical integration is nevertheless possible by using Hermitian quadrature formulas, techniques of automatic differentiation and explicit error bounds combined with interval arithmetic.