Interesting question.
The compound option is an option with K1 and T1 (mother option). The only different is its underlying asset is an option (T2,K2) (daughter option). At time to maturity, it delivers an option with maturity T2-T1, K2.
One approach suggested by the following paper (under Heston model) is to combine the MC and close form solution. Under SV model, you know the close form solution (or approximation via FT, whatever) of the option T2-T1, K2 (daughter). It should be a function of S(T1),volatility(T1). Then from 0 to T1, you can simulate the stock and volatility path so that you can calculate all the possible option prices of daughter at T1. Thus you get all the possible payoffs of mother. Average them and discount back you will get the mother's price.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1988578
I don't know whether there are some pure MC methods. At least I think the naive MC is not possible. Say if you want to get M possible outcomes of the mother option. Since conditional on each path of stock price on 0 to T1, you need to simulate another say N paths on T2-T1 to determine the daughter. This will result in a M*N number of simulation in total. This can blow up your computer. Need to find better algorithm.
best,
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