Model Risk can arise in a variety of ways. It is also an exploration of valuation algorithms and what can go wrong with them. This book is, in part, an exploration of these capabilities.

Mathematica can manage not just scalar, vector and matrix data, but also tensors of arbitrary rank and its performance scales well to large and realistic problems. In particular, version 3.0 and later includes substantial new numerical functionality, and it is capable of efficient compiled numerical modelling on large structures. Originally subtitled 'A System for Doing Mathematics by Computer', it is uniquely able as a derivatives modelling tool. One of the very few complete solutions to this list of requirements is the Mathematica system. Neither spreadsheets nor C/C++ would feature on the list, due to their fundamental failure to cope with point (i)-symbolic algebra and calculus. If one was asked afresh what sort of a system would combine together the ability to: i) deal with a myriad of special functions, and do symbolic calculus with them ii) manage advanced numerical computation iii) allow complex structures to be programmed iv) visualize functions in two, three or more dimensions and to do so on a range of computer platforms, one would come up with a very short list of modelling systems. Such option valuations may, in simpler cases, be based on analytical closed forms involving special functions, or, failing that, may require intensive numerical computation requiring some extensive programming.

The partial derivatives, expressed in financial terms, are the 'Greeks' of the option value, and may be passive sensitivity variables, or may be active hedging parameters.

Such an appreciation is most reliable when we have both a view of the local sensitivities, expressed through partial derivatives, and a global view, expressed by graphical means. We need to know not just how to work out the function (the value of an option), but also how to secure an appreciation of the sensitivity of the value to changes in any of the parameters of the function. When expressed in mathematical terms, the modelling of a derivative security amounts to understanding the behaviour of a function of several variables in considerable detail.

Mathematica for finance