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?

  • 5
    $\begingroup$ This is not exotic at all. Why don't you just bring $a$ out of the max? $\endgroup$ Commented Aug 19, 2012 at 8:31
  • $\begingroup$ 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! $\endgroup$
    – em70
    Commented Aug 19, 2012 at 13:42

1 Answer 1


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 $K/a$.


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