# FIN 4380 Economics Put Call Parity Relationship Case Study

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Use put call parity relationship to find an arbitrage opportunity.
P+S = C +PV(X)
Or P+S = C +PV(X) +D
We learned in the class that when put call parity relationship is violated, an arbitrage opportunity will
arise. You will use this case to illustrate if you can find an arbitrage opportunity in the real world. To test
the model, you will use the real data from CBOE.com options quote page to analyze the arbitrage
You may define the parameters of the put call parity or use the following assumption for the
parameters:
Interest rate is 5%
Transaction costs for a stock trade (selling or buying) is \$10 per order
Transaction costs for an options trade (selling or buying) is \$25 per order
Transaction costs for a bond trade (selling or buying) is \$25 per order
365 calendar days a year and 252 business days a year
Last trade price may be used for a stock, call, or put.
Your case report should include the following format
Introduction of the case study, explanation of any related theory, the data sources (include a snapshot
of the screen from CBOE or Yahoo finance), analytical results, and conclusion. Give a detailed
Calculate the arbitrage profit based on the transaction of one options contract.
Finally, Include everything, such as Excel calculation, in a word document.
Case One Review Example
The Put-Call Parity
c + Ke -rT = p + S0
Arbitrage Profit:
Sure profit with no risk
Real world example:
Use put call parity relationship to find an arbitrage opportunity.
P+S = C +PV(X)
We learned in the class that when put call parity relationship is violated, an arbitrage
opportunity will arise. You will use this case to illustrate if you can find an arbitrage
opportunity in a real world. To test the model, you will make 5 trades using 5 different
sets of data.
You may define the parameters of the put call parity or use the following assumption for
the parameters:
Interest rate is 5%
Transaction costs for a stock trade (selling or buying) is \$10 per order
Transaction costs for an options trade (selling or buying) is \$25 per order
Transaction costs for a bond trade (selling or buying) is \$25 per order
365 days a year
Last trade price may be used for a stock, call, or put.
Your case report should include the following format
Introduction of the case study, explanation of any related theory, the data sources, a
screenshot of the option data source, analytical results, and conclusion. Give a detailed
the arbitrage.
Finally, Include everything, such as Excel calculation, in a word document.
Step 1: Get options data
Data source: CBOE.com
The company name: BA
c=4.30
K=352.50
p=4.90
S0=353.81
r=5%
t=3 days
Step 2:
If these numbers fit the Put-Call Parity?
Arbitrage Rule: There is an arbitrage opportunity if P-C parity does not hold
c + Ke -rT = p + S0
Left side:
c + Ke -rT =4.3+352.50*e -rT =4.30+352.50*e -0.05*(3/365) =4.30+352.50*.9996
=4.30+352.36=356.66
Right side
p + S0 =4.90+ 353.81=358.71
The left is not equal to the right side. P-C parity does not hold. There will be an arbitrage
opportunity.
How to take the arbitrage opportunity? Rule: Buy Low and Sell High
Long a call and long a bond (with face value of X)
(long bond=lending money)
Short a put and short a share
Cash Flows analysis for this arbitrage:
CF
Long C
-4.30
Long bond
-352.36
Short P
+4.90
Short S
353.81
Total
\$2.05
To verify this arbitrage, we will assume two cases: the stock goes up and the stock goes
down
The CF analysis if the stock goes to
\$400
200
Long C
-4.30
+47.50 (ITM)
0 (OTM)
Long bond(lending)-352.36
352.50
352.50
Short P
+4.90
0 (OTM)
-152.50 (ITM)
Short S
353.81
-400
-200
Total
\$2.05
0
0
Step 3:
For this case, the funding requirement: use the following cash funding requirement:
Shorting stock: \$353.81
shorting Put: 4.90
Long call:
4.30
lending:
352.36
Total
715.47
\$715.37 will be required for one share trading.
How many shares am I allowed to trade? Since you are allowed to have \$1,000,000 trading capital. We
will divide \$715.37 from \$1,000,000.
\$1,000,000/\$715.37=1397 shares
One options contract allow you to trade 100 shares. You will trade 1300 shares or 13 contracts.
Total arbitrage profits: 1300*\$2.05=\$2665
after subtracting the fees:
Net Profit: \$2665-\$10-\$25-25-25=\$2580