Question

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around \(50 per share for months, and you believe it is going to stay in that range for the next three months. The price of a three-month put option with an exercise price of \)50 is \(4, and a call with the same expiration date and exercise price sells for \)7.

a. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement?

b. 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? The stock will pay no dividends in the next three months. What is the net cost of establishing that position now?

Short answer

a. Straddle Strategy

b. $11

c. $51.82

Step-by-step solution

Explanation on simple option strategy ‘a’

Straddle is simple option strategy to exploit stock price future movement. As it contains both call and put option at same strike price and expiration period.

Explanation on price movement ‘b’

Both these options would be of no use, if the price ends up at $50.

The price movement in either direction in order to make profit would have to be equal to the premium income of the straddle i.e. $11.

Explanation on creating a position involving a put, a call and riskless lending ‘c’

Position	Initial Outlay	Final Payoff
Long call	C = 7	ST < X	ST < X
Short call	-P = -4	- (50 - ST)	0
Lending	50/(1 + r)1/4	50	50
Total	7 - 4 + [50/ (1+r)1/4]	ST	ST

Assuming risk-free rate is 10%.

Net cost = 7 - 4 + [50/ (1+r)^1/4]

=$3+[50/ (1+0.10)^1/4]

=$3+$48.82

=$51.82