- DoubleTrouble
**Posts:**83**Joined:**

Hi!I'm currently reading Iain Clark's book Foreign Exchange Option Pricing and I got stuck at one sentence in the beginning of Section 3.3 that I feel is important to understand. He writes:Quote FX volatility smiles are characterized by providing volatilities, not as a function of strike, but as a function of delta. The choice of delta as the parameter describing the volatility smile is sensible, as otherwise a strike that might correspond to a considerably out-of-the-money option for small T would be very close to at-the-money for large T.where by T he refers to the time left until expiry of the option. My question is: how do you know (or argue) that just because there is an option with expiry in 1 week that is out-of-the-money a similar option (with bigger T) will be very close to at-the-money?Thanks in advance!

Well, the S&P is at 2000 now. That it should be 2200 in 1 week is unlikely yes? But 2200 in 1 year is not very far away. So both options are 200 points (or 10%) out of the money in terms of strike but the short term one is farther out of the money in terms of Delta, E(S-K)+ or probability of exercise. But it is a somewhat non-standard use of "out of the money".

Last edited by acastaldo on November 20th, 2014, 11:00 pm, edited 1 time in total.

- DoubleTrouble
**Posts:**83**Joined:**

QuoteOriginally posted by: acastaldoWell, the S&P is at 2000 now. That it should be 2200 in 1 week is unlikely yes? But 2200 in 1 year is not very far away. So both options are 200 points (or 10%) out of the money in terms of strike but the short term one is farther out of the money in terms of Delta, E(S-K)+ or probability of exercise. But it is a somewhat non-standard use of "out of the money".Thank you very much for your answer. So what you are saying is basically that:A (very) short term option that is 10% out of the money (in terms of strike) will have a delta pretty close to 0. The ATM option will have a delta pretty close to 0.5.A longer term option that is 10% out of the money (in terms of strike) will have a delta that is significantly larger than 0 but the but the ATM option will still be pretty close to 0.5-ish.So given one volatility skew, delta is a more accurate measure of how much you are in the money or out of the money compared to simply using the S/K-moneyness and hence you will pick a more realistic volatility from the surface. I have a follow-up question:Doesn't traders usually have a "full volatility surface" i.e. different skews for different expires (1w, 1m, 3m, 6m, 1y, etc). In this case, is there any advantage of using a delta parametrization? I hope this question makes senseThanks in advance!

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