Questions / Quant trading, Option pricing models
A one-step binomial call
A stock at 100 moves to 120 or 80 in one period. The real-world chance of the up move is 60%. Rates are zero. What is the price of a call struck at 100?
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Answer: 10 USD
- Risk-neutral up probability q = (1 − 0.8)/(1.2 − 0.8) = 0.5.
- The call pays 20 up and 0 down.
- Price = 0.5 × 20 = 10.
Interview shortcut. q = (1 − d)/(u − d) = 0.5, so the call is 0.5 × 20.
Takeaway. Option prices use risk-neutral probabilities, not forecasts.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.