Customer tailored derivatives: Simulation, design and optimization with the WARRANT-PRO-2 software

Abstract

Risk management is essential in a modern market economy. Financial markets enable firms and households to select an appropriate level of risk in their transactions. Risks can be redistributed towards others who are willing and able to assume them. Derivative instruments-derivatives, for short-like options or futures have a particular status. In the early 1970s Myron S. Scholes, Robert C. Merton and Fischer Black modeled an analytic pricing model for derivatives. This model is based on a continuous-time diffusion process (Ito process) for non-payout underlyings: The partial differential Black-Scholes equation. The WARRANT-PRO-2 software (Release 0.3) solves this equation with an adapted Crank-Nicholson scheme numerically. Arbitrary payments (boundary conditions) enable the design and optimization of customer tailored derivatives. WARRANT-PRO-2 computes derivative prices for given payments (simulation and expert design). But moreover this software can also optimize payments via parameterized boundary conditions of the Black-Scholes equation. The parameterized boundary conditions are optimized by nonlinear programming, i. e. an advanced SQP-method here. The deviation from a predefinable Δ of an option (performance index), e. g., can be minimized and the gradient can be computed highly accurate with automatic differentiation. A software quality and change management process for WARRANT-PRO-2, its comfortable and easy to use MATLAB-GUI (graphical user interface) and its portability to WINDOWS and LINUX operating systems is discussed. Optimized derivatives are very promising for both buyer and seller and can revolutionize modern financial markets: Examples like European double-barrier options are discussed. © 2008 Springer-Verlag Berlin Heidelberg.