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I am trying to price a quanto option by monte carlo simulation via quanto adjustment.

SDE: $dS_t^f=S_t^f(r_f - \rho \sigma_s \sigma_{d/f})dt + S_t^f\sigma_s dW_t^d$, where $S_t^f$ is the underlying asset price in foreign currency and the $r_f$ is the risk free rate in foreign currency, in domestic risk neutral measure. Should I always discount by the risk free rate of the risk neutral measure?i.e. it is in domestic risk neutral measure so I use domestic risk free rate.

I have tried to guess the risk free rate by reading the below note: The PDE (3.43) in page 32 in this note looks like it should be discounted by domestic risk free rate.

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    $\begingroup$ Use the domestic rate (the payoff is paid in the domestic currency). $\endgroup$ – Antoine Conze Jul 3 '19 at 8:25

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