Put-Call Parity and the Positive Prices of Option Premiums

Summary

The document addresses a common sign confusion in put-call parity: when constructing a synthetic forward by buying a call and selling a put at the same strike, the put’s premium is not itself negative. Option premiums are positive prices by definition; selling the put creates a cash flow in the opposite direction from buying it. Put-call parity relates the difference between the call and put prices to the discounted difference between the forward price and strike.

The short answer gives the key intuition: the call-put price difference changes sign according to whether the forward price is above or below the strike. The document also points readers to a paper on heuristic option pricing and put-call parity, but does not present its derivation or supporting details. It is a brief conceptual clarification, not a full treatment of option valuation, discounting conventions, or market frictions.

Key ideas

• An option premium is a positive price, whether the option is bought or sold.
• Selling a put reverses the direction of the cash flow rather than making the put premium negative.
• The call-put price difference depends on the forward price relative to the strike.
• Put-call parity links option prices to the forward and strike through discounting.

Tags

# What does put-call parity imply about option premiums?


# What does put-call parity imply about option premiums?












We know that $$C-P = PV(F_{0,T}-K)$$

When we create a synthetic forward, we buy call and sell a put at the same strike price $K$. When we buy the call why do we assume the premium is positive? When we sell the put, why do we assume the premium is negative?

## Answer by vonjd (score 6)

https://quant.stackexchange.com/a/1892

To see the connection between put-call parity and option price you should read this highly insightful paper by Espen Gaarder Haug & Nassim Nicholas Taleb:

> Option traders use (very) sophisticated heuristics, never the Black– Scholes–Merton formula

It shows how you can heuristically derive option pricing formulas by adapting the tails and skewness by varying the standard deviation of a Gaussian - and then remove the risk parameter by using put-call parity.

Both authors are well known in the Quant-Community, they both have an academic as well as a practical background as traders.

## Answer by Tal Fishman (score 5)

https://quant.stackexchange.com/a/1673

Both premiums are actually always positive by definition. The difference will be positive when the forward price exceeds the strike and vice versa.

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.