Wolfram Research introduced random processes in version 9 of Mathematica and for the first time users were able to tackle more complex modeling challenges such as those arising in stochastic calculus. The software’s capabilities in this area have grown and matured over the last two versions to a point where it is now feasible to teach stochastic calculus and the fundamentals of financial engineering entirely within the framework of the Wolfram Language. In this post we take a lightening tour of some of the software’s core capabilities and give some examples of how it can be used to create the building blocks required for a complete exposition of the theory behind modern finance.
Financial Engineering has long been a staple application of Mathematica, an area in which is capabilities in symbolic logic stand out. But earlier versions of the software lacked the ability to work with Ito calculus and model stochastic processes, leaving the user to fill in the gaps by other means. All that changed in version 9 and it is now possible to provide the complete framework of modern financial theory within the context of the Wolfram Language.
The advantages of this approach are considerable. The capabilities of the language make it easy to provide interactive examples to illustrate theoretical concepts and develop the student’s understanding of them through experimentation. Furthermore, the student is not limited merely to learning and applying complex formulae for derivative pricing and risk, but can fairly easily derive the results for themselves. As a consequence, a course in stochastic calculus taught using Mathematica can be broader in scope and go deeper into the theory than is typically the case, while at the same time reinforcing understanding and learning by practical example and experimentation.