Hi All,I am comparing the MTM valuations of two risk systems, with respect to FX Options. My Question is can I quantify the difference in MTMs given the following:System1: AUD/JPY, MTM = USD 461,000, Implied Vol. = 11.88%, Vega = USD 82,000, Forward Rate = 97.29 and USD Delta = -15,300,000System2: AUD/JPY, MTM = USD 406,000, Implied Vol. = 12.14%, Vega = USD 77,000, Forward Rate = 97.81 and USD Delta = -13,600,000So assuming both systems use Black Scholes (Same Model), How can I quantify the Difference in MTM (in USD) which is USD 55,000 by attributing it to: Difference in IV, Difference in Vega Risk, Difference in Fwd Rates and Difference in Delta Risk. (In other words I am trying to break down the USD 55,000 MTM Difference by IV Differences, Vega Differences, FWD Rate Differences and Delta Risk Differences)I am getting into a muddle, so was hoping somebody could please help me!Many Thanks in advanceJ.

the difference between the MTMs can be broken down approximately as followsvega = USD 21320 = 82000 * (12.14%-11.88%)/(1%) (assuming your vega is for a 1% vol change)delta = USD -81776.1 = -15,300,000 *(97.81/97.29-1) therefore MTM diff = -81776.1 + 21320 = -60456.1

Thank you so much, I guess the reason why it is an approx. change is because we are ignoring second order conditions so the Gamma and the Second order VegaMany Thanks again

Out of interest, is it possible, given the information provided to quantify the remaining differences, due to 2nd order conditions / cross greeks or is this likely to prove futile?Be amazing if I could quantify the difference in MTM as much as possible, as other FX options I am looking at have big differencesThank you

Even if you assume both systems use the same model Black Scholes (Garman Kohlhagen), the two implementations may be slightly different.For large notionals, also these differences may impact on the MTM gap.Cheers,Jordy

I would have thought the difference in MTM comes from the difference in spot (the different fwd rates tells me that the two systems are valuing with a different spot rate- it is unlikely that there are differences in interest rates between the two systems large enough to produce a difference of a half big figure in the fwd rate). The different vega's and deltas are a result of using a different spot.