The Put-Call (Options) Parity

What is the put-call parity?

The put-call parity defines the arbitrage-free relationship that determines the connection between the call premium and the equivalent put premium, under the following conditions:

• European style options
• Same underlying assets
• Same expiry
• Same strike

Given a call premium the put premium must be at a level consistent with Put-Call Parity so that the actual futures price and the synthetic futures price are identical, excluding transaction costs.

How do we calculate the fiduciary call?

Fiduciary call - Protective put. This relationship can also be expressed as;

call premium plus present value of the strike equals put premium plus stock.

What is one of the keys to understanding the Put-Call Parity?

• The understanding that by combining positions in two out of the following three elements Future, call and put, we can synthetically create a position in the third element
• It can be encapsulated in the simple expression, F = C – P. What this says is that a long futures position plus F, can be synthetically created by combining a long call plus C and a short put minus P
• By rearranging the expression we can get all six combinations, reflecting the long and short positions for each. For example, buying a call and selling a future gives us a long put position.  Similarly selling a future and selling a put gives us a short call position