The potential traps fall into two categories. The first category contains problems arising from the complexity of some models, leading to their being seriously error prone in their implementation, even if not intrinsically flawed. The second category contains algorithms that are intrinsically flawed. These are the partial derivatives of the option value with respect to the underlying price and other variables such as time and interest rates. A more subtle type-one difficulty relates to the computation of implied volatility, which is a favorite parameter of traders.
Implied volatility makes sense only for the simplest vanilla options.
In other cases, the implied volatility may be unstable, double valued, or triple valued or may even possess infinitely many values. In Mathematica the graphical tools can be used to test this very quickly. Some quite well known algorithms are intrinsically flawed. Problems which we might identify as a type-two issue can be found in the following models. These are essentially numerical methods, and the book looks in detail at them in comparison with exact solutions for known cases.