I'm trying to price an option with payoff $\max\{a\cdot S_t - K,0\}$ where $a$ is a known constant. Ideally I'm looking for a closed form, continuous-time solution. Where should I begin?
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5$\begingroup$ This is not exotic at all. Why don't you just bring $a$ out of the max? $\endgroup$– Alexey KalmykovAug 19 '12 at 8:31
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$\begingroup$ because I was too tired to realize I could, I suppose. thanks, now it looks quite trivial, actually. if you post it as an answer, I'll mark it accepted! $\endgroup$– em70Aug 19 '12 at 13:42
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The payoff $\max\{a\cdot S_t - K,0\}$ can be re-written as $a\cdot\max\{S_t - K/a,0\}$. Therefore it can be priced as a regular call option with the strike $K/a$.
answered Aug 19 '12 at 17:10