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Why Quant Models Use Unrealistic Assumptions

Original question

Why do quantitative finance models make assumptions that are clearly unrealistic in actual financial markets?
Models simplify markets so a specific question can be answered, calibrated, and tested with the data available. An assumption is useful when it preserves the features that matter to that decision and gives errors you can assess. An assumption becomes dangerous when it removes a feature that drives the result, such as trading costs in a high-turnover strategy or jumps in the pricing of far-out-of-the-money options.

What a simplified model buys you

A pricing model with constant volatility is easier to fit and explain than a model with many moving parameters. That simplicity can make it useful as a common benchmark. If the task is to compare prices across strikes, a constant-volatility assumption may leave persistent differences that point toward a richer model. Extra realism also has a cost. New parameters need data, may be poorly identified, and can amplify estimation error.
Ask what the decision depends on. A model meant to estimate a typical daily move may work with assumptions that fail in the tails. A model used for capital stress or barrier risk needs evidence about extremes, path dependence, and the scenarios where the approximation fails.

Put the sensitive assumption under pressure

  1. State the decision and the horizon. An intraday execution decision and a one-year risk estimate depend on different information.
  2. Identify the sensitive assumptions. Alter one at a time. For example, vary trading costs, introduce a jump, or raise the assumed correlation during stress.
  3. Compare with a benchmark. Use held-out observations, quoted prices, or an independent method appropriate to the decision. Explain how input differences affect the comparison.
  4. Report the limits of use. Record where the model was fitted, the situations it handled well, and which scenarios produced material errors. Set a review threshold that matches the stakes of the decision.

A useful validation exercise can end with the simple model if the added complexity improves little for the decision at hand. In another application, the same exercise can expose why the simple model fails.

Consider two hypothetical models for daily returns. Model A is Gaussian with mean zero and standard deviation 1%. Model B has a 2% chance of losing 5%, a 2% chance of gaining 5%, and a 96% chance of no change. Both have mean zero. Model B also has variance 0.04(0.05)2=0.00010.04(0.05)^2=0.0001, so it has the same 1% standard deviation as Model A.

Under Model A, the 99th percentile of daily loss is roughly 2.33%. Under Model B, the 99th percentile is 5%. Matching the first two moments leaves a large difference in tail risk. If the model is used for a tail decision, matching daily standard deviation alone offers weak validation. A historical stress exercise or a model with heavier tails would address a feature the first fit discarded.

The example also tells you what to ask a model owner. If the decision is a rough variance budget, equal variances may be enough for the immediate job. If the decision depends on a rare one-day loss, you need evidence about the tails and how uncertain your tail estimate is. Write down which decision changes when the assumption changes. That's more informative than a blanket claim that the model is realistic, and it gives you a concrete reason to spend effort on a richer model.