Case One Review
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.
THIS IS HOW CALCUATIONS WERE PERFORMED. (COMPARE THIS TO EXCEL FILE IN “ANALYTIC RESULTS” PORTION in PARAGRAPH 2)
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
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
Buy left and sell right 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
How much trading credit do you need for one share trading:
For this case, the funding requirement: one for one:
Shorting stock: $353.81
shorting Put: 4.90
Long call: 4.30
lending: 352.46
Total 715.47
$715.47 will be required for one share trading.
How many shares am I allowed to trade? $250,000/715.47=349.42
300( 3 contracts)
Total arbitrage profits: 300*$2.05=$615
Net Profit: $615-$10-$25-25-25=$530
WRITTEN REPORT DETAILS (VERY IMPORTANT!!!)
Your case report should include the following format:
Paragraph 1
Explain:
- put call parity relationship
- what happens when it is violated
- how an arbitrage opportunity will arise.
Paragraph 2
Explain:
- the data sources (screenshot of the option data numbers in excel file)
- analytical results: please explain the excel file calculations in (see excel file for data)
Paragraph 3
Conclusion:
- Give a detailed description on one of your trades and the other four briefly. Assume you have $1,000,000 trading capital to conduct the arbitrage.
I HAVE FAITH YOU WILL DO WELL IN THIS REPORT. BELIEVE IN YOURSELF AND TRY YOUR HARDEST. I AM PROUD OF YOU. REMEMBER TO REFER TO THE EXCEL FILE ATTACHED!
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