Question

Suppose you are interested in investigating the option price efficiency of Altria Group, Inc. (MO) listed options. You look at options expiring in January of 2020, which is close enough to one quarter for your purposes. You observe the following prices listed for the options (below). Are the options efficiently priced, how do you know (2 pts)? Hint look at a box spread with strikes at $60 and $70. If the options are not priced correctly, ignoring trading costs, what is the arbitrage profits that could be made from the trade? (2 pts) The risk-free rate is 1.5%

Strike Last Price

60.00 4.90

62.50 3.47

65.00 2.35

67.50 1.50

70.00 0.99

Puts

60.00 2.20

62.50 3.18

65.00 5.20

67.50 8.05

70.00 9.82

Answer 1

A short box spread is done by selling a bear call spread and selling a bull put spread with the same strike prices. That is :

• Sell the $60 call - premium received is $4.90
• Buy the $70 call - premium paid is $0.99
• Sell the $70 put -   premium received is $9.82
• Buy the $60 put - premium paid is $2.20

Net premium received = $4.90 - $0.99 + $9.82 - $2.20

Net premium received = $11.53

Profit of short box spread = net premium received - (higher strike price - lower strike price)

Profit of short box spread = $11.53 - ($70 - $60)

Profit of short box spread = $1.53

Yes, there is an arbitrage opportunity and the options are not price efficiently.

Present value of arbitrage profit = profit of spread / (1 + risk free rate)^t,

where t = time to expiration in years. This is 3/12, since the options expire in one quarter.

Present value of arbitrage profit = $1.53 / (1 + 1.5%)^3/12

Present value of arbitrage profit = $1.524