Recently I was asked: “Are you not afraid of over-reliance on numerical methods in finance?”
Indeed, if I had to rely on numerical results in finance, I would be afraid.
Take counterparty risk as an example. There are three popular numerical measures of counterparty risk: exposure at default, loss given default and probability of default. Firstly, it would be wrong to hope that just three numbers fully describe our risk. Secondly, numerical results inevitable depend on the mathematical model that we use. A model is always imprecise, but we seldom know by how much we are off. Thirdly, once we have chosen a model, we have to calibrate it. We can calibrate to market data, to historical data, or some mix of those. In either case, we essentially try to predict the future based on market consensus (i.e. public opinion) or history. Neither is a reliable predictor, as everyone knows.
Does it mean that numerical results are useless? Not at all. For example, correlation is not a perfect measure of statistical dependency; still, it is useful in many cases. Likewise, it is useful to know our potential exposure on each counterparty. After all, we need to know how much cash we need to reserve to cover our losses in case of default, and potential exposure gives us a number. We are not sure that this number is exact (in fact, we are sure it isn’t), but at least we have a starting point.