The common stock of the C.A.L.L Corporation has been trading at a narrow range a
ID: 2456520 • Letter: T
Question
The common stock of the C.A.L.L Corporation has been trading at a narrow range around $50 per share for months, you believed it is going to stay in that range for the next 3 months. The price of a 3 month put option with the exercise price of $50 is $4.
a.) if the risk-free rate is 10% per year, what must be the price of a 3 month call option on C.A.L.L. stock with the exercise price of $50 if it is at the money. (the stock pays no dividends)
b.) what would be a simple option strategy using a put and a call to exploit your conviction about the stock price's future movement? what is the most money you can make on this position? how far can the stock price move in either direction before you lose money?
c.) how can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? what is the net cost of establishing that position now?
Explanation / Answer
(a)
By using put call parity,
Price of call option = P + S – X/(1+r)t
P = price of put option = $4
S = Stock price = $50
X = Exercise price = $50
R=rate of interest = 10%
T = Time = 3/12 years
Price of call option = $4 + $50 - $50/1.103/12 = $54 - $48.82 = $5.18
(b)
Sell a straddle, i.e., sell a call and a put to realize premium income of =$5.18 + $4 = $9.18
If the stock ends up at $50, both of the options will be worthless and your profit will be $9.18. This is your maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put. The stock price can move by $9.18 in either direction before your profits become negative.