### Model Risk

A while back, I went to a get-together with Massimo Morini, who wrote a book on model risk specifically. It struck me as a really interesting concept. I’ve been meaning to write a few words on model risk since.

Model risk is the risk of a significant difference between the mark-to-model value of an instrument, and the price at which the same instrument is revealed to have traded in the market, according to Rebonato.

There can be often a couple of different ways to calculate it. In physics, where you have different mathematical approximations for a specific phenomenon, you will calculate roughly the same value.

In finance, you’re often working from quite different assumptions that don’t necessarily overlap. Let’s say you use two different models. Each one will probably give you values which are significantly different. You can be calculating a value for exactly the same thing, and get completely different values.

In fact, it’s quite a serious problem. At the moment that you need this value to make decisions, you don’t know to what extent you’re using the right model. It’s not enough to be doing exactly the right calculation.

Those numbers are often different enough from one another that it’s almost impossible to know where the real value would be in a certain situation. This puts you into a funny situation, because even though you have these seemingly rigorous mathematical models, usually if you do need to make a decision, you’re forced to fall back to intuition anyway.

What you can do is look at the range of values produced by all relevant models. That gives you a sense of where the actual value of say, the price of an option is–where it actually lies. You can be reasonably confident that the value is somewhere in that interval. In reality, however, the value of the option is as much as anyone is willing to pay you for it.

You might trick yourself into thinking you’re using these really sophisticated mathematical approaches. It always comes back to the same simple rules that you’ll see everywhere else. If you go to a local street market, the value of the fruit sold is what people are willing to pay for it.

This behaves unpredictably is when there’s a rapid change. For example, all of the sudden, market consensus changes very quickly. The price of a particular instrument plummets. Let’s say that instrument is used as an input into the value of derivatives.

For example, Morini mentioned the mortgage CDOs during the subprime crisis. As long as house prices were rising, all models gave roughly the same values for mortgages. Once the rise of housing prices reversed, all models disagreed. Regardless of which model you were using, you obtained different values for the price of a particular mortgage. The event made it very difficult to look at which model was the best model to evaluate what the values of these CDOs are. Paradoxically, you need to know the values of the instruments most during such an event.

I think a lot of people get caught up with the math. They think that because it’s mathematical it’s very precise and sophisticated. Moreover, they know that mathematical models can explain a number of physical phenomena quite well.

In finance, though, the math sometimes gets in the way the basics. You need to knowing exactly where you are. You need to know exactly what’s happening in the market. There are certain relative arbitrage opportunities which keep things in balance during normal market conditions.

None of this holds when the market goes “tits up”. All correlations go to one. You lose “resolution”.At that point, this model risk shows how fragile using this mathematical approach actually is. During a crash all correlations go to one, everything goes crazy, and this point, the models are pretty much worthless.