Put Call Parity Model
1
The prices of European puts and calls
on the same stock with identical
exercise prices and expiration dates
have a special relationship. The put
price, call price, stock price, exercise
price, and risk-free rate are all related
by a formula called put-call parity

2
Variable Definitions
C = call premium
P = put premium
S0 = current stock price
S1 = stock price at option expiration
E = option striking price
R = riskless interest rate
t = time until option expiration

3
The Put/Call Parity Relationship
 We now know how the call prices, put
prices, the stock price, and the riskless
interest rate are related:
t
r
E
SPC
)1(
0



4
The Put/Call Parity Relationship
 The interpretation of this is as follows:
– Buying a call and shorting a put is the same as:
– Buying the stock and borrowing E (the exercise
price) at the risk free rate
t
r
E
SPC
)1(
0



5
The Put/Call Parity Relationship
(cont’d)
Equilibrium Stock Price Example
You have the following information:
 Call price = $3.5
 Put price = $1
 Striking price = $75
 Riskless interest rate = 5%
 Time until option expiration = 32 days
If there are no arbitrage opportunities, what is the equilibrium
stock price?

6
The Put/Call Parity Relationship
(cont’d)
Equilibrium Stock Price Example (cont’d)
Using the put/call parity relationship to solve for
the stock price:
18.77$
)05.1(
00.75$
00.1$50.3$
)1(
365
32
0



 t
r
E
PCS

7
The Put/Call Parity Relationship
A stock trades at $50 with a six month put option
(strike price=$50) trading at $4.25. If the interest
rate is 3%, what is a six month call option trading
at?
98.4$
25.450
)03.1(
50$
)1(
5.0





C
C
PSo
r
E
C t

8
The Put/Call Parity Relationship
A stock trades at $60 with a put option (strike
price=$60) trading at $2.75. If the call option trades
at $5.35, what is the interest rate?
%5.4,
045.11
)1(
60$
35.5$75.2$60$
)1(
1






rTherefore
r
r
r
E
CPSo t

9
Making Arbitrage Profits
A stock trades at $25 with a put option (strike price=$25) trading at
$3.00. If the call option trades at $3.50 and the interest rate is 5%,
how do I make a riskless profit? How much of a profit do I make for
each share traded?
Buy stock, buy put, short call, borrow money
Profit per share = $24.75-$23.81 = $0.94
81.23$
)05.1(
25$
75.2425.3$00.3$25$
)1(
1




 t
r
E
CPSo

Thank you
10