28 Frequently Asked Questions In Quantitative Finance
What is Put-Call Parity?
Short Answer
Put-call parity is a relationship between the prices of
a European-style call option and a European-style put
option, as long as they have the same strike and expira-
tion:
Call price−Put price=Stock price
−Strike price (present valued from expiration).
Example: Stock price is $98, a European call option
struck at $100 with an expiration of nine months has
a value of $9.07. The nine-month, continuously com-
pounded, interest rate is 4.5%. What is the value of the
put option with the same strike and expiration?
By rearranging the above expression we find
Put price= 9. 07 − 98 + 100 e−^0.^045 ×^0.^75 = 7. 75.
The put must therefore be worth $7.75.
Long Answer
This relationship,
C−P=S−Ke−r(T−t),
between European calls (valueC) and puts (valueP)
with the same strike (K) and expiration (T)valuedat
timetis a result of a simple arbitrage argument. If you
buy a call option, at the same time write a put, and sell
stock short, what will your payoff be at expiration? If
the stock is above the strike at expiration you will have
S−Kfrom the call, 0 from the put and−Sfrom the
stock. A total of−K. If the stock is below the strike at
expiration you will have 0 from the call,−Sagain from
the stock, and−(K−S) from the short put. Again a total
of−K. So, whatever the stock price is at expiration this
