How Delta Hedging Relates to Put–Call Parity

Summary

The discussion explains how a forward used to delta hedge a vanilla option can be represented synthetically with options. Under put–call parity, a short forward position corresponds to a short call and a long put at the same strike and expiry. The example considers buying a 10 million notional 30-delta call and selling 3 million of the matching forward; the response describes the combined exposure as 7 million of calls and 3 million of puts at that strike.

A second answer cautions against treating the forward itself as an option: it is an over-the-counter obligation, its value at issuance is zero by definition, and put–call parity is a relationship among options. The synthetic interpretation is therefore a way to express the hedge exposure using parity, rather than a claim that the forward contract literally is an option. The short exchange offers an intuition and an example, but does not state assumptions such as discounting, dividends, or settlement conventions.

Key ideas

• A forward position used to delta hedge can be represented synthetically through put–call parity.
• A short forward corresponds to a short call and a long put with matching strike and expiry.
• The example combines a long call with a short forward into call and put exposures.
• A forward remains an obligation rather than an option, despite its synthetic option representation.

Tags

# Delta Forward and Put Call Parity


# Delta Forward and Put Call Parity












Vanilla options are traded interbank with delta hedge. The instrument employed to a delta hedge is usually a forward with the same expiry (and opposite delta) as the option. This means that in effect the traded instrument is a call and a put with the same strike.

Why is that so and how does the Put Call Parity fit in here?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/54147

If Bank A buys 10mm of a 30 delta call from Bank B, then sells 3mm of the forward to Bank B as a delta hedge, then you can think of the 3mm delta hedge as (short 3mm call plus long 3mm put) using put call parity. Therefore , the overall trade can be thought of as : bank A buys 7mm of a call and 3mm of a put at the same strikes from bank B. Is this what you are looking for ?

## Answer by user24980 (score 0)

https://quant.stackexchange.com/a/54135

- not exactly, a forward is an otc obligation, not an option

- the price of a forward at issuance is 0 by definition

- the parity holds for options only

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