Question

# You would like to be holding a covered call position on the stock XYZ. The stock...

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?

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

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