Risk-Neutral Pricing
The mathematical trick behind every option pricing model on every desk
Run an experiment. Ask ten professional options traders what they think the S&P 500 will return over the next year. You will get answers ranging from negative ten percent (the bears) to positive fifteen percent (the bulls), with the median somewhere around the long-run average of plus eight or nine percent.
Now ask the same ten traders to price a one-year SPY option. You will get answers within a fraction of a cent of each other. Same people, same instrument, same time horizon, completely different dispersion.
The reason is one of the most counter-intuitive results in modern finance: when traders price options, they all use the same expected return for the underlying. It is not eight percent. It is not ten percent.
It is the risk-free rate — the same number a Treasury bill pays. They all know the stock will not actually earn that return on average; they all believe stocks earn an equity risk premium over Treasuries.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 7 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1Why we can use a fictional probability and still get the right answer
- 2Risk-neutral probability is NOT a probability forecast
- 3The pricing formula in risk-neutral form
- 4Risk-neutral vs. real-world ITM probability — long-dated SPY 5% OTM call
- 5Why every Monte Carlo pricer in production uses the risk-neutral measure
- 6Where to see this on the platform
- 7Summary