Lesson 20 of 20 · 7 min

What a pricing model can and cannot tell you

A model converts assumptions into numbers; it cannot tell you whether the assumptions hold.

This closing lesson is about calibration — not of the model, but of your confidence in it. Both failure modes are common: dismissing the model because its assumptions are false, and trusting its output because it has decimal places.

What a pricing model does reliably:

Enforces internal consistency. Put-call parity and no-arbitrage relationships hold, and violations are usually data errors.
Translates prices into comparable units, so a contract can be compared across strikes, expiries and underlyings.
Quantifies sensitivities. Delta, gamma, theta and vega are useful even when the level of the price is disputed.
Makes assumptions explicit. Every input is stated, so a disagreement can be located in a specific number.

What it cannot do:

Forecast the underlying. Expected return is not even in the formula.
Tell you the correct volatility. That input is inferred from prices or estimated from history, and both are contestable.
Price the tails. Lesson 19 showed the failure is orders of magnitude, not percentages.
Account for liquidity. A price the model produces may not be obtainable in any size.
Say whether a position is appropriate for anyone. That is not a question a pricing model has any content about.

The honest summary is that a model is a consistency engine. Feed it assumptions and it returns their implications without arithmetic mistakes. If the assumptions are wrong, it returns wrong answers with the same fluency, and nothing in the output flags the difference.

Take the risk you can measure. A model tells you what your assumptions imply — which is the measurable part. Knowing which assumptions you are relying on is the rest of the work.

Key terms

Model output: The implication of a set of assumptions. Its reliability is bounded above by the reliability of the weakest input.
Sensitivity analysis: Re-running a model across a range of inputs to see which ones actually move the answer. Usually more informative than the base case.
False precision: Reporting more digits than the inputs justify. A price stated to the cent from a volatility guessed to the nearest five points.

Worked example

How much of the answer is the assumption

The base-case 30-day at-the-money call, repriced across a plausible range of volatility estimates.

Volatility 20%: $2.45
Volatility 25%: $3.02
Volatility 30%: $3.59
Range of model prices: $2.45 to $3.59
Precision of the volatility input: Rarely better than ±5 points
Defensible way to state the output: About $3, not $3.02

The model reports two decimal places from an input known to within five points. The decimals are real arithmetic and false precision at the same time.

Check yourself

A model prices a contract at $3.02. The volatility input is uncertain by about five points either way. How should the output be stated?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.