Hi everybody,

I was trying to show in the lines of "funding beyond discounting" that the PV of a domestic claim [$]V_T[$] collateralized in foreign currency is given by

[$]V_t = E^Q \left[ e^{- \int_t^T r_{cfor}(s) ds} \frac{X_t}{X_T} V_T \right][$]

where [$]r_{cfor}[$] is the foreign collateral rate, [$]X_t = X_t^{dom/for}[$] is the FX rate and [$]Q[$] the measure associated with my domestic funding rate [$]r_F[$] (or the corresponding bank account).

My thoughts are that at every point in time t I receive/pay [$]V_t[$] as collateral, which has to be converted into foreign currency [$]\tilde{V}_t = \frac{V_t}{X_t}[$] (probably I receive/pay [$]\tilde{V}_t[$] straight away), earns [$]r_{cfor}[$] and has to be converted back into domestic currency with [$]X_{t + \delta t}[$].

However, I'm struggling to put that into the equation

[$]V_t = E^Q \left[ e^{- \int_t^T r_F(s) ds} V_T + \int_t^T e^{- \int_t^s r_F(u) du} (r_F(s) - ...) V_t ds \right][$]

Does anybody have a solution or hint for me?

Thanks,

Bernd