Quantitative Finance

Emanuel Derman’s Guide for the Perplexed Quant

I came across and was reading Emanuel Derman’s article titled “A Guide for the Perplexed Quant“.

Emanuel Derman is one of the originators of the Black-Derman-Toy interest rate model and the Derman-Kani local volatility model, and was a Managing Director at Goldman Sachs running its quantitative strategies research group. He is now a professor at Columbia University.

There are many good points in the article, and should be read by students of quant finance, or PhDs entering the field of quant finance.

Below are the points that I find most interesting.

Most Financial Models are Toys Based on Analogy

  • Most widely used yield curve models in finance are phenomenological models. Phenomenological models are built to describe and draw inferences from data, but there is a toy-like quality to their description. They work by a pragmatic analogy that one hopes is descriptive and useful, but one doesn’t delude oneself into thinking it’s the truth.

Financial Modelling is Never Going To Be Very Accurate

  • In finance, you are playing against agents who value assets based on their feels about the future in general and their future in particular; these feelings are ephemeral, or at best, unstable, and fresh news on which they are based keeps streaming in.
  • When you propose a new financial model, you’re pretending you can guess the structure of another person’s mind. When you try out a simple yield-curve model, you’re implicitly saying something like ‘Let’s pretend that people care only about future short rates, and that people expect them to be distributed log-normally.’.. You know immediately that there is no chance you are truly right.
  • Regard models as a collection of parallel thought universes you can explore. Each universe should be consistent, but the real financial and human world is going to be much more complex than any of them. You’re always trying to shoehorn the real world into one of them to see how useful that approximation is.
  • Fisher Black: “In the end, a theory is accepted not because it is confirmed by conventional empirical tests, but because researchers persuade one another that the theory is correct and relevant.”

 Models Should Have Factors That You Can Opine About

  • Better to have market models with variables and factors you can name and whose nature you can grasp and opine about, than to have black-box models that dictate actions without a perceived structure.
  • You’re always trying to make a limited approximation of reality, with perceptual variables you can think about, so that you can say to yourself, or your boss, ‘I was short emerging market volatility, so we lost money’

Traders Have to Learn to Think in Terms of the Model’s Parameters

  • Because models turn parameter estimates into prices, the person using the model has to have a visceral feel for the parameters and their dynamics.
  • Modellers have to learn to build models that cater to a trader’s natural mental framework.

Complex Models Doesn’t Necessarily Improve Things

  • A usable model has to provide both input and a way of speaking that comes naturally.
  • New quants on Wall Street often are amazed at the naiveté of Black-Scholes, and immediately try to do better by adding jumps, stochastic volatility, correlations, transaction costs, etc. However if your foundation is an opinion, and therefore necessarily vague, don’t build a house of cards on it.
  • What works are simple low-dimensional models with a few essential characteristics. Most real things are too messy for a full theoretical treatment, and that’s why implied values, which mask so many unknowns in one effective calibration parameter, play such a large role.
  • The more factors you need to calibrate to, the less useful your model.

Optimization Has Limited Value

  • In financial theory, each scenario is imprecisely wrong — there’s a crude interest rate model, a crude prepayment model, and other misspecifications. While averaging may cancel much of the misspecification, optimization tends to accentuate your lack of knowledge.

What Constitutes a Good Financial Model

  • Good theories, like Black-Scholes, provide a theoretical laboratory in which you can explore the likely effect of possible causes.
  • You must always ask: does the model give us a set of plausible variables to use in describing the world, and a set of relationships between them that we can use to analyse and perturb the world?
  • [Quants] are involved in intuiting, investing or concocting approximate laws and patterns… to paint a picture of how to think qualitatively, and then within limits, quantitatively, about the world of human affairs, and in so doing, have an impact on how other people think.


Emanuel Derman has a related article with Paul Wilmott, titled The Financial Modelers’ Manifesto (link here). He makes similar points

  • Models are tools for approximate thinking, they serve to transform your intuition about the future into a price for a price for a security today. It’s easier to think intuitively about future housing prices, default rates and default correlations than it is about CDO prices.
  • The CDO research papers apply abstract probability theory to the co-movements of thousands of mortgages. The relationships between so many mortgages can be vastly complex. The modelers, having built up their fantastical theory, need to make it useable; they resort to sweeping under the model’s rug all unknown dynamics; with the dirt ignored, all that’s left is a single number, called the default correlation.
  • We like simplicity, but we like to remember that it is our models that are simple, not the world.
  • You must start with models and then overlay them with common sense and experience.




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