Question 25: A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears. Delta Hedging a Short Call using Stocks and Debt Days to maturity (Tin days) Description Symbol 30 29 28 Spot price ($) 5 100 101 98 Strike price (5) K 95 95 95 Risk free cont. comp. rate (pa) r 0.1 0.1 0.1 Standard deitiation of the stock 5 cont. comp. o 0.3 0.3 03 returns (pa) Option maturity (years) T 0.082192 0.079452 0.076712 Delta N[d1] = dc/dS 0.768815 0.805239 0.694289 Probability that S > K at maturity In risk N[d2] 0.741812 0.781103 0.664565 neutral world Call option price (5] c 6.986185 7.711617 Stock investment value ($1 N[d1]*S 76.881509 81.329178 ,Bormwmg Wh'Ch pa'" funds 5m" N[d2]*K/e"(r*T) 69.895324 73.617561 ? investment ($) Interest expense from borrowmg paid in r*N[d2]*K/e"(r*T) 0.019152 ? arrears (5) Gain on stock ($1 N[d1]*(SNew - SOld] 0.768815 ? Gain on short call option (5) -1*(cNew - COId) -0.725431 Net gain (3) Gains - InterestExpense 0.024232 Gamma r = d"2c/dS"2 0.035406 0.032258 0.043061 Theta B = dc/dT 23.038272 22.287334 24.972017 In the last column when there are 28 days left to maturity, some values are missing. Which of the following statements about those missing values is NOT correct? (a) The call option price is expected to be 355.389.1127. (b) The stock investment value used for hedging should be $660403, partly funded by $62.651174 in debt. (c) The interest expense on the borrowing from the previous day will be $0.020172. *(d) The gain on the stock is -$13.288878 (note the negative) and the gain on the short call option is $232249. (e) The net gain is -$0.1134 (note the negative). Page 18 of 23