Bets and decisions · Trading desk
Pays if it ever touches
A stock closes today at $100. On each of the next 10 trading days its close moves exactly $1 up or $1 down, each with probability 1/2, independently of every other day. A contract pays $100 if the stock closes at $103 or higher on at least one of those 10 days, and nothing otherwise. What is its fair price, in dollars?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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