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Nested event contracts

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Contract A pays $1$ if event E happens. Contract B pays $1$ if both E and a second event F happen, so B can never pay when A does not. A can be bought at an ask of $0.40$ and B can be sold at a bid of $0.45$ . A trader buys $200$ units of A and sells $200$ units of B. What is the smallest profit the trader can end up with across all outcomes?

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Hint

Find the worst outcome for the trader among the cases for E and F.

Solution

If E fails, both contracts pay $0$ and the trader keeps the price gap $0.45 - 0.40 = 0.05$ per unit.
If E and F both happen, both pay $1$ and the result is also $0.05$ per unit; if E happens without F the result is higher at $1.05$ .
The smallest profit is $200 \times 0.05 = 10$ .

Answer: $10$

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