Actuarial FM question: Please show steps, final answer is a)call payoff = 0 when

Question

Actuarial FM question:

Please show steps, final answer is

a)call payoff = 0 when S_T=80 or 90, =10 when S_T=105
  call profit= -2.04 when S_T=80 or 90, =7.96 when S_T=105

  b) S_T> 107.0396

At time 0, the share price of a stock was $85. At that time, a call option on a share of stock with a strike price of $95 expiring 6 months later had a premium $2.00. Risk free interest is 4% annual effective. (a) Determine the payoff and the profit on the purchased call option on the expiry date for each of the following stock values at time T = 0.5: 80, 90, 105. (b) Determine the share price needed on expiry to obtain a profit on the purchased call option of at least $10.

Explanation / Answer

price on the expiry date                          80                 90                105

strike price                                            95                 95                 95

status of call option                               lapse            lapse        exercise

Gross payoff                                       0                      0                10 (105-95)

profit                                                 -2.04(2*1.02)       -2.04           7.96 (10-2.04)

note : interest is 4% per annum, so for sixmonths is 2%

for buying of call option we have to pay premium so it is loss on our part

at the st of 80/90 call option is not exercised so the pay off is zero

B) share price on expry to get profit of 10 is

               = profit + premium + interest on premium paid + strike price

               = 10 + 2 + ( 2*2%) + 95

               = $107.04

so profit = 107.04 - 2.04 - 95     = $10

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