Mathematica and the Future of Derivatives Pricing

William Shaw
Nomura International plc

This presentation will survey the role of Mathematica in the pricing of complex financial instruments. Derivative securities normally require the calculation of a function of several variables together with a large set of partial derivatives. This places considerable strain on both traditional programming languages and the algorithmics required. The talk will show how Mathematica streamlines all stages of the modeling process from the elementary computation of partial derivatives through to the exposure of subtle flaws in well-known numerical algorithms. The use of advanced special-function techniques and the exploitation of the compiler will also be demonstrated, as will the use of the kernel in conjunction with Excel.

William Shaw is the director of the Quantitative Analysis Group of Nomura International plc, London. He is author of Applied Mathematica, Complex Mathematica, and the forthcoming Cambridge University Press text Modeling Financial Derivatives with Mathematica. Shaw has demonstrated that even standard textbook formulations for the valuation of derivative financial instruments have potentially serious flaws which can be investigated and corrected using Mathematica.