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In, out and the vanilla · Part 3 of 3
One-year calls on a stock at $100 have a strike of $100; rates are zero and volatility is 20%, so the vanilla call is worth $7.97. Barrier versions have a barrier at $90, monitored continuously.
With zero rates, the down-and-in call satisfies C_di = (S/H) × C(H²/S, K), a vanilla on a reflected stock price. What is the down-and-in worth? Take N(−0.954) = 0.1701 and N(−1.154) = 0.1243.
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
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