Question

You would like to be holding a covered call position on the stock XYZ. The stock XYZ is currently selling for $120. Over the next year, the stock price will either increase by 10% or decrease by 10%. The exercise price of the call option is $125. The risk free interest rate is 3% per year.

A. What is the price of the call option? (Use a one-period binomial model)

B. What is the cost of the covered call portfolio? What will be the payoff and profit on the covered call portfolio at a stock price of $140?

Answer 1

A.

If the stock price increases by 10%, stock price at maturity = (1+10%)*120 = $132

If the stock price decrease by 10%, stock price at maturity = (1-10%)*120 = $108

Call option payoff if the stock price increases by 10% = 132-125 = $7

Call option payoff if the stock price decreases by 10% = 0

Price of the call option is the discounted expected payoff

Price of the call option = 0.5*7*e^(-0.03*1) + 0.5*0

Price of the call option = $3.397

B.

Covered call consists of a long position in stock, and a short position in a call option

Covered call cost = $120- $3.397 = $116.603

Hence, the cost = $116.603

Payoff if the stock price of $140 = (140-120) - (140-125)

Payoff if the stock price of $140 = $5

Profit on the covered call = $(140-120-(140-125)+3.397)

Profit on the covered call = $8.397