Mathematicians have an ability to think clearly and precisely that is rare among finance professionals. We’re excellently placed to provide model validation consulting services. Learn how I found a critical conceptual error in risk modelling work by one of the largest financial consulting firms in the world.
There are two main kinds of models that quantitative analysts are called on to validate in the financial services: derivative pricing models, and risk models.
Validating derivative pricing models
Much of derivative pricing theory is now completely standard and well-worn. This means that there is no question, in principle, of how to price certain derivatives. Validating derivative pricing models is thus often mainly about checking the correctness of the coding implementation. A standard way to do this is to build a second, independent model against which to compare the output of the original model. Since it’s impossible to run the two models with all possible inputs, usually one would try to generate a set of test parameters which cover every significant discrete case, such as each possible ordering of date parameters and date coincidence. Another important step is to compare the behaviour of the model to the produce description, as just because the two models agree does not necessarily mean they are correctly implementing the intent in the product description.
However, not all derivatives can be priced with a well-known and standard method. Barrier derivatives can require careful work to ensure the model is converging correctly. Custom derivatives can arise which require some ingenuity to price. Examples like high-dimensional derivatives with a large number of underlying assets can require novel mathematics to price, as standard methods are simply not fast enough on current computer hardware. As mathematicians, we’re excellently place to help you price these bespoke derivatives.
See also our derivative pricing consulting services.
Validating risk models
If pricing derivatives mainly involves applying existing theory, designing and validating risk models can be much more creative. There is no standard way to estimate financial risk, and, in our experience, much of the risk modelling work in the financial services industry is of very little value. We can build bespoke risk models, taking into account data limitations, that will be of far higher quality than what you could get from most major consulting firms.
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