What are the limits of financial models and simulations? A quant speaks.

An interview on 11 February 2005 in Trading Markets with Dr Emmanuel Derman raises some interesting points about the validity of models and simulations. Dr Derman is a quant on Wall Street, with a background as a physicist, applying higher mathematics to investment banking.

Financial modelling ought to be simple: all the inputs and results are already in numerical form, and massive amounts of data are readily available.

However, in four quotes from the interview Dr Derman adresses some of the assu,ptions behind financial modelling processes.

“…when you propose a new model of value, you’re pretending you can guess the structure of another person’s mind. When you try out a new yield curve model, you’re implicitly saying something like “Let’s pretend people in markets care only about the level of future short-term interest rates, and that they expect them to be distributed normally.” As you say that to yourself, if you’re honest, your heart sinks.”

“…Where do models enter? It takes a model to show that the two different securities are similar, meaning that they have identical future payoffs under all circumstances. To demonstrate payoff identity, (1) you must specify what you mean by “all circumstances,” for each security, and (2) you must find a strategy for creating a replicating portfolio that, in each future scenario or circumstance, will have identical payoffs to those of the target….Most of the mathematical complexity in finance involves the description of the range of future behavior of each security’s price…”

“Most financial models are models by analogy, I’m afraid, and analogies are always imperfect. It’s amazing that physics works as well as it does, quite mind-boggling….

Black-Scholes is perhaps closest to a fundamental model, but it’s really a piece of brilliant engineering, a recipe. Black-Scholes tell you how, under certain idealized but not totally ridiculous assumptions, you can create a stock option out of a (dynamic, constantly changing) mixture of money invested in stock and money invested in an interest-bearing bank account….”

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