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I've started to try and find some more exotic options to try and price using general results about the Black-Scholes equation.

One of the more interesting ones I came across is the call-on-a-put option with strike $K_1$ and expiry $T_1$. It gives the holder the right to buy a given underlying put option at time $T_1$ for the price $K_1$. Suppose the put option has strike $K_2$ and expiry $T_2$ s.t. $T_2>T_1$. How am I supposed to price this option on $t<T_1$?

At time $T_1$ we have that the value of the call option is $(P(S,T_1)-K_1)^+$ where $P(S,T_1)$ is the value of the underlying put option. Hence, we can use the BS equation to find the price of the call.

Is this a valid reasoning? It seems a bit odd to me

Any tips and general suggestions on where to read about pricing in general are more than welcome!

asdf
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    You can use BS to find the price of the put option at time $T_1$ given the price of the underlying at that time. But to find the price of the call option, the BS formula will not be OK. You have to go back to computing an expectation under the risk neutral measure. – Raskolnikov Jun 07 '18 at 19:45
  • Wouldn't it suffice just to use Feynman-Kac's formula? – asdf Jun 07 '18 at 22:10
  • That's just another word for risk neutral valuation in this case. – Raskolnikov Jun 08 '18 at 09:17
  • By the way, if you google "compound option pricing", there are already two articles popping up on the very first page that describe how to proceed. – Raskolnikov Jun 08 '18 at 09:18

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