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.
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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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