Question

The common stock of the Orange Incorporated 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 at-the-money put option on Orange Incorporated is $5.

a. If the risk-free interest rate is 2% per year, what must be the price of a 3-month at-the-money call option on the Orange Incorporated stock? (Note: ATM options are the options for which the strike price is equal to the current stock price.) The stock pays no dividends.

b. What would be a simple options strategy to exploit your conviction about the stock price’s future movements? To receive a full credit, you should i. Identify which options are involved in your strategy ii. Construct a payoff table and show it in this exam iii. Show payoff of your strategy on a graph

c. How far would the price of the Orange Incorporated have to move in either direction for you to make a profit on your initial investment?

Answer 1

a]

As per the put-call parity equation, C + (K/(1 + r)^t) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values to find the price of the call option

C + (K/(1 + r)^t) = P + S

C + ($100 / (1 + 2%)^3/12) = $5 + $100

C = $5.49

b]

i]

To exploit your conviction about the stock price’s future movements, a long straddle position should be taken.

This involves simultaneously buying an ATM put option and an ATM call option with the same strike price and expiration.

In this case, the $100 call and put options would be bought simultaneously.

ii]

Payoff of a long call option = Max[S-K, 0] - P

Payoff of a long put option = Max[K-S, 0] - P

where P = premium paid.

iii]

c]

Upper breakeven = strike price + total premium paid

Lower breakeven = strike price - total premium paid

total premium paid = price of call option + price of put option

Upper Breakeven = $100 + $5 + $5.49 = $110.49

Lower Breakeven = $100 - ($5 + $5.49) = $89.51