## ATM strike of fx vol surface

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### ATM strike of fx vol surface

Hi Mark,

Do you have any idea on how to build a fx vol surface which allows the middle point (ATM strike) to change with expiry tenors? Say for a currency pair, for expiry below 10 years the vol surface is built using delta neutral strike as the ATM middle point, and for expiry longer than 10 years the vol surface is built using forward as the ATM middle point. Then for an expiry between 10 years and 11 years ( assuming 10y and 11y are the two adjacent banchmarks ) you need to interpolate in the time space from the 10y and 11y benchmark vols (+-25, +-10, and ATM, but ATM means different thing for 10y and 11y ). Suppose at this expiry tenor the delta neutral strike is already lower than the -25 delta strike so you cannot build a vol smile using delta neutral strike.

One possible approach is to interpolate in the strike space on the 10y smile to get the ATM forward vol for 10y, and directly get the ATM forward vol for 11y, and then interpolate in the time space to get the ATM forward vol for this expiry, and use this as the ATM middle point to build the vol smile for this expiry. But this might cause some unwanted significant jump in the price of two vaniilas with the same strike and different but very close expiries, say 10y and 10y plus one day, due to the change in the ATM middle point of the vol smiles. Any ideas to solve this issue to improve the smoothness? What approaches have been used in market practice to build a vol surface allowing the ATM strike to vary with the expiry tenors?

regards,
nbzx

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