The relationship between the price of a European call option and European put option is known as put-call parity.
This equation states that a portfolio of a long call option and a short put option is equivalent to a single forward contract at the same strike price and expiry.
The value of long options (calls) increases with an increase in interest rate, while the value of short options (puts) decreases.
Therefore, long calls and short puts have a positive rho, while long puts and short calls have a negative rho.
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Interest rate increases usually increase the value of long options – calls – and decrease the value of short options – puts. Therefore, long calls and short puts have a positive rho; long puts and short calls have a negative rho.
Rho - Overview, Positive and Negative Rho, Option Types
Put-call parity is an important concept in options pricing which shows how the prices of puts , calls , and the underlying asset must be consistent with one another. This equation establishes a relationship between the price of a call and put option which have the same underlying asset.
What is the Put-Call Parity? - Corporate Finance Institute
In financial mathematics, put – call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that…
Put–call parity - Wikipedia
Put-call parity: The relationship that exists between call and put prices of the same underlying, strike price and expiration month. Conversion: An investment strategy in which a long put and…
Put/Call Parity - optionseducation.org