Question

Consider a 1-year one period European call option where X = 26. The stock price is currently $24 and at the end of one year it will be either $30 or $18. The risk-free interest rate is 5%.

a. What position in the stock is necessary to hedge a short position in one call option? (5 points)

b. Assume C is equal to $2.86, what is the possible values of the portfolio you created in part (a) above at expiration (hint, find Vu and Vd)? (5 points)

Answer 1

a) For a short call position, you need to buy one stock at the price $24

Hence, the portfolio would consist of one 1 short call at strike price $26 and one long share bought at $24

b) If the stock price ends up at $30

Loss from the short call = -$(30-26+2.86) = -$6.86

Profit from long call = $(30-24) = $6

Total loss = -$6.86+ $6 = -$0.86

If the stock price ends up at $18

Profit from the short call = $(0+2.86) = $2.86

Loss from long call = -$(24-18) = -$6

Total loss = -$6+ $2.86 = -$3.14

Expected loss PV = (0.5*(-$0.86) + 0.5*(-$3.14))*e^(-0.05*1) = -$1.90