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Perpetual option interview question

biooil

Joined
1/14/14
Messages
6
Points
11
A classic problem: A perpetual (i.e. expiry is infinity) American digital option pays $X if it hits $B at any time, and $0 otherwise. Assuming interest rate is zero, how do you use Black-Scholes equation to price it? (hint: first derive that the option price is linearly dependent on asset price, then use some boundary conditions to solve it.)
 
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