MAF308 Derivatives and Fixed Income- Ratio Call Writing

Question 1.  (This question has three parts: I, II, and III)

There is an option involved strategy named “Ratio call writing”. It is the strategy when one owns a certain number of shares of the underlying stock and simultaneously sells calls against more shares than one owns. Therefore, there is a ratio of calls written to stock owned. The most common ratio is the 2:1. For example a 2:1 ratio can be established by buying 100 shares of ABC at $49 per share and selling 200 ABC October 50 calls at $6. 

Part I.

What is the profit/loss of the above “ratio call writing” strategy when stock price at October expiration is $37, $45 and $63, respectively? (4 Marks)

Part II.

For the above strategy, what is the expected maximum profit and when can the maximum profit be achieved? What is the expected maximum loss and when are you likely to suffer the loss? Would the strategy break even at October expiration? At what range of stock prices, do you expect to make profit? (4 Marks)

Part III.

The following is a common objection to the strategy “ratio call writing”:  “why bother buying 100 shares of stock and writing 200 calls? You will be naked writing 100 calls. Why not just sell 100 naked calls?”  Do you agree with this objection that the above strategy is the same as “selling 100 naked calls”? Please justify your response.  (6 Marks)

Question 2. (This question has three parts: I, II and III) 

A stock price is currently $80. Over each of the next two six-month periods, it is expected to go up by 6% or down by 6%.  The risk-free interest rate is 5% per year with semi-annual compounding.  

Part I.

Use the two-steps binomial tree model to calculate the value of a one-year American put option with an exercise price of $80. (5 Marks)

Part II.

Is there any early exercise premium contained in price of the above American put option? If there is, what is the early exercise premium?  (3 Marks)

Part III.

Discuss how you can hedge risk if you write the above put option with an exercise price of $80 and 1-year maturity. 

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