2001 the first version WARRANT-PRO-2 (0.1) has been presented, see Breitner and Burmester (2002), which optimizes cash settlements for European double-barrier options and warrants. From the viewpoint of financial mathematics, some of the boundary conditions of the partial differential Black-Scholes equation are parameterized. The Black-Scholes equation is solved with a numerical Crank-Nicholson scheme and the parameters are optimized by nonlinear programming, i. e. an advanced SQP-method. In the upgraded version WARRANT-PRO-2 (0.2) an option?s deviation from a predefinable Delta (performance index) is minimized. The global error order of the Crank-Nicholson scheme is now quadratic in time (option's time to maturity) and space (market price of the option's underlying). The gradient of the performance index is computed highly accurate with automatic differentiation. Now a MATLAB-GUI (graphical user interface) allows easy evaluation, design and visualization of options and warrants. WARRANT-PRO-2 (0.2) and its GUI run stand-alone on LINUX PCs and laptops. Optimized options can combine the advantages of futures and options. Delta can be made almost constant for long periods and for a wide range of underlying market prices. Thus, no Delta-hedge adaptation is required. Moreover, tedious margining is not necessary. Optimized European double-barrier options are very interesting derivatives for both buyer and issuer and can revolutionize modern financial markets, see also www.iwi.uni-hannover.de/warrantpro2.html .
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Paper provided by Institut für Wirtschaftsinformatik, Universität Hannover in its series IWI Discussion Paper Series with number
5.