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Under the Black-Scholes framework, there is a closed form formula for the price of a compound options, as first derived by Geske (1979). However, the analytical formula refers to a critical stock price, which is the value of the stock at expiration date of the compound option such that the (underlying) option is at the money at the expiration date of the compound option.

Just to confirm: even though the formula for the compound option is "analytical", the evaluation of it still requires Monte Carlo as the critical stock price is not known in advance (at the time of pricing), is this correct?

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    $\begingroup$ You can determine the critical strike price with a solver like Newton-Raphson $\endgroup$
    – David Duarte
    Commented Sep 21, 2020 at 17:15
  • $\begingroup$ Ah, of course! Silly of me, it is as you say that simple because under BS the vol is constant. $\endgroup$
    – user34971
    Commented Sep 22, 2020 at 5:41

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