Correct Measure for FX Simulation in PFE

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Correct Measure for FX Simulation in PFE

Postby magassi » Tue Jun 17, 2014 3:37 am


I am a bit puzzled by this. I want to calculate the potential future exposure of a two FX forwards in one year time. One is on CC1/CC2 and another is on CC2/CC1. Please note that both quotes are exactly the same except that they are quoted in different diection, i.e. one is per unit of CC1 and another is per unit of CC2. I want to calculate PFE in 1 year by simulation, i.e. I need to calculate the value of the two FX forwards in one year time at the 95% percentile. To do this, I will need to simulate FX rate (say 1000 paths) to one year time and use the simulated FX rate to plug into my FX forward pricing formula. PFE is obtained by finding the the values at the 95% percentile. My question is that what is the correct measure, i.e. CC1 or CC2, that I should use to simulate the FX rate. That is, if we let S=CC1/CC2 (CC1 as per unit of CC2) and S'=CC2/CC1 (CC2 as per unit of CC1), should I use dS = (rCC1 - rCC2)Sdt + vol*SdW and dS' = (rCC2 - rCC1 + vol^2)S'dt + vol*S'dW or should I use
dS' = (rCC2 - rCC1)S'dt + vol*S'dW' and dS = (rCC1 - rCC2 + vol^2)Sdt + vol*SdW'? W is the CC1 measure and W' is the CC2 measure. Obviously, the simulated FX rates S and S' will be different depending on which sde I use. Thanks for the help.
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