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How Market Conventions Define At-the-Money Options

Article Quant Q&A · Author: FrancescoD
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Summary

The discussion asks whether a long-dated at-the-money straddle should use the strike nearest spot or the strike nearest the forward. The answer is that “at the money” depends on the market and product convention. Foreign exchange volatility quotes may define ATM through a delta-neutral straddle, with several spot or forward and premium-adjustment variants. Listed options on futures may use a forward-based framework such as Black-76.

The response cautions against assuming that ATM always means a 50-delta strike. In the stated formula, when strike equals forward, positive volatility contributes a positive term to d1, so the call delta exceeds 50 under the stated convention. Another answer describes ATM straddles as commonly having zero net delta, while a conflicting response equates ATM with 50 delta. The material offers conceptual guidance and a formula, but no complete market-by-market convention table; traders should check the convention for the instrument they are trading.

Key ideas

  • The meaning of an at-the-money option depends on asset class and market convention.
  • A forward-at-the-money strike need not correspond to a 50-delta option.
  • Foreign exchange volatility conventions can define ATM using delta-neutral straddles and different adjustment methods.
  • For options on futures, a forward-based pricing framework may be used.
  • Confirm the applicable convention before selecting a strike for an ATM straddle.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Is “at the money” referent to the spot or forward price?


# Is “at the money” referent to the spot or forward price?












This may be a trivial question, but one I wasn’t sure about. Imagine I want to buy a 1 year ATM straddle. Does “at the money” imply buying closest to the current spot price, or does it mean to buy at the strike closest to the forward price. Was curious because I was looking at some option chains and for longer maturity options the spot ATM is something like 60/40 deltas rather than 50/50, which is usually a couple strikes higher.

## Answer by AKdemy (score 3, accepted)

https://quant.stackexchange.com/a/65922

I guess generally what ATM means depends a lot on asset classes. FX vols are quoted as ATM DNS (delta neutral straddles). This in itself can be Spot, Forward, Spot premium adjusted, forward premium adjusted with the following formulas retrieved from the working paper FX volatility smile construction :

However, based on your wording I assume you think 50D would be ATM. That is just a common misconception. Since you write option chains, I assume it is listed and not FX stuff. If you for example look at commodity, these are usually options on futures. Hence modelled with Black76 - greeks are here at the end. In a simple example where I solved for 50D beforehand, you can see how far from ATMF the 50D is when vol is high. The below was done with Julia.

Generally, if $\delta = N(d1)$ excluding discounting, and $d1 =( log(F/K) + 0.5*σ^2*t ) / (σ*sqrt(t))$, you can see that for 100% moneyness, hence $F=K$, $d1>0$ which means it is above 50D which corresponds to N(0.0). It is an increasing function of vol:

## Answer by river_rat (score 0)

https://quant.stackexchange.com/a/65901

For straddles ATM usually implies 0 delta. In general, ATM is determined by the market conventions in question.

## Answer by Tradier_Quant (score -1)

https://quant.stackexchange.com/a/65902

When referring to a long straddle, atm means the 50 delta strike.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.