Put Call Parity

This movie/ video explains the concept of Put-Call Parity in the CFA exam. Please refer too "Introduction to Call Option", Introduction to Put Options and Protective Put for the basics. The following is the transcript.

 

 

Put-Call parity is very useful in estimating the value of the call (c) or put options (p) if one of them and also the stock price (S) and risk free bond (B) future value are known. The relationship is derived by forming a protective put and a fiduciary call. A protective put has been mentioned in the previous talk which is by holding a stock S and longing a put option.

 

For a fiduciary call, we long a call option together with holding a risk-free bond. The call option also has a striking price at X and the bond has future value B=X at maturity. Also, the bond, the call and the put options should have the same maturity.

 

You can see that fiduciary call has the same shape as a protective put. This means that they have the same portfolio values to the investor upon maturity. Therefore, to prevent any arbitrary opportunity, the price of the fiduciary call and the protective put must be the same! This means that the present prices of the call (c) and put (p) option have to satisfy the following equation:

 

X/(1+r)T+c = p + S

 

where X is the striking price (also the bond future value), c and p are the call and put option prices respectively and S is the current stock value. This is the put-call parity. And you can use it to estimate p, for example, if c, S, X, r, T are known.

 

In summary, when using the put-call parity, make sure that the bond, call and put options have the same maturity and the same striking prices and the bond future value are the same.

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