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Why ATMF FX Straddle Call and Put Deltas Can Differ

Article Quant Q&A · Author: babaji
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Summary

The document asks why the absolute call and put deltas of an at-the-money-forward foreign-exchange straddle may differ, and whether the difference follows from the lognormal assumption in Black–Scholes. The response points to premium-adjusted delta as a possible explanation: adjusting delta for the option premium, expressed in the foreign currency, can make the call and put deltas unequal in magnitude.

The answer refers to a formula for premium-adjusted at-the-money-forward delta and specifies that its sign parameter is positive for calls and negative for puts, but the formula itself is absent from the supplied text. It therefore offers a plausible convention-based explanation rather than a full derivation or a worked example. The document does not establish that the lognormal model causes the observed difference, and it gives no market data or comparison with other FX delta conventions.

Key ideas

  • Premium-adjusted FX delta can differ from unadjusted delta because it accounts for the option premium in foreign currency.
  • The response identifies premium adjustment as a possible reason at-the-money-forward call and put deltas differ in absolute value.
  • The sign parameter in the referenced formula is positive for a call and negative for a put.
  • The supplied text omits the formula, so it does not show a full derivation or confirm the effect of the lognormal assumption.

Tags

ForexOptionsDerivatives pricing
Full text
# ATMF FX straddle delta


# ATMF FX straddle delta












I am trying to price an ATMF FX (say Usdidr) straddle - the fxdelta for call and put leg are quite different with put fxdelta being higher than call delta. (Absolute values) Why would this be the case? Is this related to distribution being assumed as log normal in black scholes model?

Thanks in advance.

## Answer by Magic is in the chain (score 0, accepted)

https://quant.stackexchange.com/a/41646

These could be premium adjusted deltas. Essentially the delta would have been adjusted by the amount of the option premium in foreign currency. Re-comment, here is the formula for the premium adjusted ATMF delta (note \phi=1 for call and -1 for put):

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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