# Fight Finance

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A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of$12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

 European Options on a Non-dividend Paying Stock Description Symbol Put Values Call Values Spot price ($) $S_0$ 10 10 Strike price ($) $K_T$ 12 7 Risk free cont. comp. rate (pa) $r$ 0.05 0.05 Standard deviation of the stock's cont. comp. returns (pa) $\sigma$ 0.4 0.4 Option maturity (years) $T$ 1 1 Option price ($) $p_0$ or $c_0$ 2.495350486 3.601466138 $N[d_1]$ $\partial c/\partial S$ 0.888138405 $N[d_2]$ $N[d_2]$ 0.792946442 $-N[-d_1]$ $\partial p/\partial S$ -0.552034778 $N[-d_2]$ $N[-d_2]$ 0.207053558 Gamma $\Gamma = \partial^2 c/\partial S^2$ or $\partial^2 p/\partial S^2$ 0.098885989 0.047577422 Theta $\Theta = \partial c/\partial T$ or $\partial p/\partial T$ 0.348152078 0.672379961 Which of the following statements is NOT correct? 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 Description Symbol Days to maturity (T in days) 60 59 58 57 56 55 Spot price ($) S 10000 10125 9800 9675 10000 10000 Strike price ($) K 10000 10000 10000 10000 10000 10000 Risk free cont. comp. rate (pa) r 0.05 0.05 0.05 0.05 0.05 0.05 Standard deviation of the stock's cont. comp. returns (pa) σ 0.4 0.4 0.4 0.4 0.4 0.4 Option maturity (years) T 0.164384 0.161644 0.158904 0.156164 0.153425 0.150685 Delta N[d1] = dc/dS 0.552416 0.582351 0.501138 0.467885 0.550649 0.550197 Probability that S > K at maturity in risk neutral world N[d2] 0.487871 0.51878 0.437781 0.405685 0.488282 0.488387 Call option price ($) c 685.391158 750.26411 567.990995 501.487157 660.982878 ? Stock investment value ($) N[d1]*S 5524.164129 5896.301781 4911.152036 4526.788065 5506.488143 ? Borrowing which partly funds stock investment ($) N[d2]*K/e^(r*T) 4838.772971 5146.037671 4343.161041 4025.300909 4845.505265 ? Interest expense from borrowing paid in arrears ($) r*N[d2]*K/e^(r*T) 0.662891 0.704985 0.594994 0.551449 ? Gain on stock ($) N[d1]*(SNew - SOld) 69.052052 -189.264008 -62.642245 152.062648 ? Gain on short call option ($) -1*(cNew - cOld) -64.872952 182.273114 66.503839 -159.495721 ? Net gain ($) Gains - InterestExpense 3.516209 -7.695878 3.266599 -7.984522 ? Gamma Γ = d^2c/dS^2 0.000244 0.00024 0.000255 0.00026 0.000253 0.000255 Theta θ = dc/dT 2196.873429 2227.881353 2182.174706 2151.539751 2266.589184 2285.1895

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?