AstraZeneca plc (AZN) stock was trading at $45 on August 16, 2011 and the follow
ID: 2808376 • Letter: A
Question
AstraZeneca plc (AZN) stock was trading at $45 on August 16, 2011 and the following options prices are available:
Sept 40 put - $1.50
Sept 50 put - $6
Sept 40 call - $6
Sept 50 call - $1
Consider a long box spread using AZN by buying a bull call spread and buying a bear put spread. Answer the following questions.
A) What is the cost of the bull call spread?
B) What is the cost of the bear put spread?
C) What is the value of the box spread on expiration date. Assume the expiration is on Sept 16?
D) If the risk-free annual interest rate is 4%, is there an arbitrage opportunity? If so, explain a strategy to profit from the market condition and show the amount of arbitrage profit from your strategy.
Explanation / Answer
A) A bull call spread is an option strategy that involves purchasing a call option and simultaneously selling another call option with the same expiration date but a higher strike price.
In this case will buy the call option with strike price 40 (Sept 40 call) and sell the call option with strike price 50 (Sept 50 call). We will spend $6 (Sept 40 call) and receive $1 (Sept 50 call).
Total cost = $6 -$1= $5
B) A bear put spread is an option strategy that involves purchasing a put option and simultaneously selling another put option with the same expiration date but a lower strike price.
In this case will buy the put option with strike price 50 (Sept 50 put) and sell the put option with strike price 40 (Sept 40 put). We will spend $6 (Sept 50 put) and receive $1.5 (Sept 40 put).
Total cost = $6 -$1.5= $4.5
C) Box spread is an option trading strategy that involves purchasing a bull call spread with a corresponding bear put spread.
Value of the box spread on expiration date = Higher Strike Price less Lower Strike Price in the spread = 50-40 = $10.
Profit will be $10 regardless of where the stock's price is at expiration date.
D) Since the total calculated cost of the box spread ($5 + $4.5= $9.5) is less than the expiration value ($10), a risk-free arbitrage is available with a box strategy implemented.
To exploit this arbitrage opportunity, borrow $9.5 at risk free rate. Buy a box spread by paying those $9.5. Sell the box spread at expiration value of $10, on expiration date, i.e. one month from now. Pay the interest on $9.5 borrowed. Interest= 9.5*(1+0.04)1/12 - 9.5 = $0.0311.
Amount of arbitrage profit = Expiration value - Cost of box spread - Interest paid = 10 - 9.5 - 0.0311 = $0.4689
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