Question

You are looking at option prices on calls and puts and noticed that Biogen Idec (BIIB) is currently selling at $319.55. You look up the price of a call and a put with a strike price of $300 and maturing in 6 months. The price of the call is $40.80 and the put is $19.25. Assume BIIB does not pay a dividend. You also noticed the risk free rate is 2% per annum with continuous compounding for the next six months. If there is a mispricing, generate an arbitrage that will allow you to exploit this mispricing otherwise show that no arbitrage can be made. What do you long and what do you short? How much money will you make by just entering into the arbitrage buying/selling one share of the securities you need to exploit the mispricing? (Assume you face no transaction costs.)

a. Assume these are European options.

b. Assume these are American options.   

(Looking for an answer in Excel, work shown please)

Answer 1

SOLUTION:-

A) For european options :

We can check with put call parity if there is an arbitrage opportunity exists.

As per put call parity:

• C + PV of cash required to make the call = P + Spot price
• Fiduciary call is : 40.8 + 300*exp(-0.02*180/365) = 337.85
• Protective put is : 19.25 + 319.55 = 338.8
• So the two values are not equal.

Protective put is over priced and need to be shorted, and finduciary call needs to be bought to make arbitrage profit of $1 which is the approx. gap between the two.

B) For American Options:

Such an opportunity wont exits as they can be exercised at any point of time, and thus any such opportunity will not exist in the market, as the same will be equalized immediately.

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