FX Option Delta Hedge Equivalence Under Put-Call Parity

Summary

The note explains why FX option market makers may describe positions in terms of long or short strikes rather than whether the option is a put or a call. With a delta hedge included, put-call parity makes a put position equivalent to a call position, so the combined positions carry the same underlying risk exposure.

The explanation relies on the assumption that the underlying FX asset is readily tradable with negligible friction, allowing the hedge to be established immediately. Under that assumption, the equivalence follows from replication and parity. The note does not derive the option deltas or discuss how hedge costs, market frictions, or differing conventions affect the relationship, so it is a brief conceptual answer rather than a full treatment of FX option risk.

Key ideas

• Put-call parity relates a put combined with an underlying hedge to a call.
• The delta-hedged put and call have equivalent risk exposures under the stated assumptions.
• The explanation assumes the underlying FX asset is liquid and can be traded with negligible friction.
• The note does not quantify the effects of transaction costs or market conventions.

Tags

# Delta in FX Options markets


# Delta in FX Options markets












In several FX options textbooks, the authors explain that put-call parity combined with the fact that FX option market makers trade options with a delta hedge included, means that it does not matter if a put or a call is traded, but rather if it is a long or short strike.

Both a put and a call will have the same delta exposures.

Does this mean that both a put and a call have positive delta, and if so, how come?

## Answer by user68819 (score 1)

https://quant.stackexchange.com/a/80570

The answer is in the question. A put with a delta hedge (by put call parity) = call. Assume delta is a close to frictionless asset and immediately tradeable, therefore a put and a delta hedge is a call and vice versa.

Therefore, it follows if a put plus delta hedge is equivalent to a call it must have exactly the same risk too.

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.