Embed Size (px)
DESCRIPTION
Citation preview
1
Put Call Parity Model
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:
tr
ESPC
)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
tr
ESPC
)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(
36532
0
tr
EPCS
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
PSor
EC
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
ECPSo
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
tr
ECPSo
10
Thank you
