Question

An options exchange has a number of European call and put options listed for trading on ENCORE stock. You have been paying close attention to two call options on ENCORE, one with an exercise price of $52 and the other with an exercise price of $50. The former is currently trading at $4.25 and the latter at $6.50. Both options have a remaining life of six months. The current price of ENCORE stock is $51 and the six-month risk free rate is 3% p.a., continuously compounded.

Required:

How would you exploit this situation to earn arbitrage profits? You should assume the arbitrageur can borrow or lend at the risk free rate, can short sell shares if necessary and does not face any transaction costs.

Hint: For call options with different strike prices but the same expiration date, the maximum difference between call prices is C₁– C₂ < (K₂– K₁) e^-rTwhere K₂> K₁. You are expected to employ the five-step proof method to demonstrate your arbitrage strategies. When demonstrating the arbitrage opportunity, you will need to consider different scenarios at time T, ie., if  , , and  .

Answer 1

Assuming there is no change in stock price in 6 months, strategy would be long 52 price option and short 50 price option. Net premium earned is 2.25

Case 1) stock price increases, let's say price is at 60

Buy options cancel each other and we would have net income of 0.25

Case 2) stock price decreases, let's say price is at 40

No options is exercised and we have net income of 2.25