Let us assume we have two FX rates: $ 1 EUR = S_t^{(1)} USD$ and $ 1 GBP=S_t^{(2)} USD $. Let $K_1>0, K_2>0$ be strictly positive values and a payoff at some time $ T>0 $ (called maturity) defined by: $ V_T=1_{ \{ \kappa_1\cdot S_T^{(1)}<\kappa_1\cdot K_1 \} } \cdot 1_{\{\kappa_2\cdot S_T^{(2)}<\kappa_2\cdot K_2\}} , \kappa_1,\kappa_2\in\{-1,+1\}$. We know that this product is dependent on the correlation between the two FX rates. HJow do trading desks measure the exposure to this correlation parameter? How do they hedge such options?
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Dispersion trading is a way to mitigate correlation risk. The book "Foreign Exchange Option Pricing A Practitioners Guide" (Chapter 10 Multicurrency Options) introduces an analysis framework. Last, people use the gap to smooth out the barrier regarding digital options. i.e. using call/put spreads to replicate digital payoffs.
