Bets and decisions · Options · difficulty 3 of 5
Paid either way
A stock trades at $100. Each day it moves exactly $1 up or $1 down, each with probability 1/2, independently of other days. A contract pays, after 10 days, the distance between the stock price and $100 in dollars, whichever direction it moved: a final price of $96 or $104 both pay $4. What is the contract's fair price, in dollars, meaning its expected payout?
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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