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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

trading. Assume you have $1,000,000 trading capital to conduct 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

description of one of your trades and the other four briefly.

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

description of one of your trades. Assume you have $250,000 trading capital to conduct

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

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

Step 3:

How much trading credit do you need for one share trading:

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

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