Let us denote the upper and lower barrier levels by $B$ and $b$, respectively. The payoff of the knock-out hurdle double knock-in barrier call option can be defined as follows:

$$\left(S_T-K\right)^+\mathbb{I}_{\{L\leq S_{T_h}\leq U\}}\mathbb{I}_{\{\left(H^{B,b}\leq T\right)\}}$$

where $U$ and $L$ are the upper and lower hurdle levels. Hence, we have a knock-in option with barriers being active until expiry with a knock-out double hurdle level active on the hurdle date $T_h$. The payoff is similar to a window double barrier, but unlike that one the hurdle levels are only active on a single day instead of having a time window of activation of barrier. Do you have any suggestion on how to replicate the payoff and/or price via PDE this contract with stochastic volatility?



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