Put-Call Parity Applies to Matched Options, Not an Entire Portfolio

Summary

The note clarifies the scope of put-call parity for a portfolio containing long and short European calls and puts at different strikes. Parity is a no-arbitrage relationship for a call and put with the same underlying, strike, and expiration, together with the underlying asset and financing terms. It is therefore checked on matched contracts; there is no single portfolio-wide parity measure that equates options with different strikes or maturities.

For assessing how a portfolio changes with market conditions, the answer points instead to option sensitivities, or Greeks. These describe exposures such as changes in value with the underlying price, volatility, or time, and can help compare distinct positions. The example notes that selling a put with similar delta can create stock-like directional exposure to a long call. This is only a local sensitivity comparison: equal delta does not make positions equivalent in all scenarios, and parity itself does not measure overall portfolio risk or similarity.

Key ideas

• Put-call parity is defined for a call and put with the same strike and expiration.
• A portfolio with options at different strikes does not have one aggregate parity relationship.
• Option Greeks provide a way to compare sensitivities and assess portfolio exposure.
• Similar delta can imply similar directional exposure, but it does not make two positions fully equivalent.

Tags

# Is it possible to calculate the call-put parity for an option's portfolio?


# Is it possible to calculate the call-put parity for an option's portfolio?












Let's say I have designed an option's portfolio. The portfolio includes long as well as short positions in European-style put and call contracts based on the same underlying asset with different strike prices.

Does it make sense to calculate the call-put parity for pairs of call and put with the identical strike prices? or is there is an approach to calculate the call-put parity for the option's portfolio as as a measure of the equivalence between call and put contracts?

## Answer by meh (score 1, accepted)

https://quant.stackexchange.com/a/30449

The put-call parity is just a no-arbitrage condition that exists for options at the same strike and expiration. If you want to know how your portfolio will change or how similar two options are you are going to want to look at the greeks. https://en.wikipedia.org/wiki/Greeks_(finance)

As an example, if you want long exposure to a stock but don't want to buy a call option you could sell a put option with a similar delta.

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.