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!