Questions / Quant trading, Options & hedging
A one-step replicating model
A stock is 100 now and will be 120 or 80 in one step. Rates are zero and there are no dividends. What is the no-arbitrage price of a European call with strike 100?
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Answer: 10 price
- Risk-neutral up probability is (100 − 80)/(120 − 80) = 1/2. Expected call payoff is 0.5 × 20 = 10.
Interview shortcut. Risk-neutral q = (100 − 80)/(120 − 80) = ½, so price = ½ × 20.
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