June 29th, 2018, 11:12 am
Since the knockout is only at expiration then the payoff of the option can be written as
[$] \theta (X_T - K) \theta (L - V_T) [$]
where [$] \theta [$] is the Heaviside function, [$] X_T [$] is exchange rate at maturity, [$] V_T [$] is the realised variance at maturity, and [$] K, L [$] are the strikes. Agree?
Let's assume first that the realised variance and exchange rate are independent. The price of the option is then
[$] E_t [\theta (X_T - K)] E_t [\theta (L - V_T)] [$]
which is. the product of two digital options. Hence, to hedge the total option you'll need to hedge using both FX forwards and variance swaps, or alternatively dynamically rebalance a vanilla FX digital by an amount equal to the vanilla FX variance / vol digital (if those are traded at all).
In the case where the correlation is non-zero you'll have a bit more work to do.
Hope this helps.