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 $25per order. Assume 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 put-call parity as well as the use of put - call parity for arbitrage,the data sources, analytical results, and conclusion. Give a detailed description of one of your trades and explain why your trade will generate an arbitrage profit. Assume you have $100,000 to conduct the arbitrage.

Example:

Put Call parity:

C+PV(EX)=P+S

If Put Call parity is violated, there will be an Arbitrage opportunity.

S=$152.42

C=$6.1

P=3.20

EX=150

R=5%

T=2 month

C+PV(EX)=P+S

Left= C+PV(EX)=6.1 + 150/1.05^(2/12)=6.1+150/1.00816=6.1+148.79=154.89

Right=P+S=3.2+152.42=155.64

Is the right = Left?

Left (154.89) < Right (155.64)

There is an arbitrage opportunity.

Rule: Buy Low and Sell High

Long: Call Long: Bond with face value=EX=$150 (Price =148.79 calculated above)

Short: Put Short: Stock

At t=0 CF₀

Long: Call -6.10 Long: Bond -148.79

Short: Put +3.2 Short: Stock +152.42

Profit +$.73

You are given $100,000 to do the trading.

For simplicity, one share trading requires (Left (154.89) < Right (155.64)) $154.89+$155.64=$310.53

$100,000/310.53=322 shares ----- choose 300 shares ---3 contracts of options call or put

So total profit will be 300*$.73=$219. Net profit=$219-cost of trading=219-10-25-25-25=$134

S=$200 $100

At t=0 CF₀

Long: Call -6.10 200-150=+50 0 Long: Bond -148.79 +150 +150

Short: Put +3.2 0 -50 Short: Stock +152.42 -200 -100

Profit +$.73 0 0