The common stock of the STABBLES Corporation has been trading in a narrow price

Question

The common stock of the STABBLES Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a three-month call option at an exercise price of $100 is $10.

Part A: If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on STABLES stock at an exercise price of $100? The stock pays no dividend.

Part B: What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment? (The answer to this question should include a payoff table for your strategy and a graph to support your argument).

PLEASE SHOW ALL FORMULAS AND CALCULATIONS. THANK YOU.

Explanation / Answer

From the put-call parity, we know that

P = C – S + [X/(1 + r)^t].

P = $10 - $100 + [$100/(1.10)^(1/4)] = $7.645 is the put option price

B

You need to buy a straddle which means buying both a put and a call option on the stock.This would require total cost of $10 + $7.645 = $17.645, this is also the amount which the stock need to move in up or down for the profit on the either option side to cover the investment costs.Please note that this does not include the time value cost.To consider time cost, the stock price would need to swing in either direction by $17.645 x (1.10)1/4 = $18.07.

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