Question 3 (9 marks) Consider the following information about a non-dividend paying stock: The current stock price is $36, and its return standard deviation is 30% per year. The continuous compound risk-free rate is 3% per year. Assume that the Black-Scholes model correctly prices all the options written on the stock given the information above. a). A call option written on the stock expires in 1 year and has an exercise price of $36. Calculate the Black-Scholes value of the call option using the provided cumulative normal density table with arguments rounded to two decimal places. (3 marks) I b). A put option written on the stock expires in 1 year and has an exercise price of $36. Find the value of the put option using your answer in part a). (2 mark) c). You find that a risk-less zero-coupon bond that pays $36 in 1 year is currently priced at $35.50. Assume that you can buy and short sell i) the stock at $35.50 and ii) the call and put options at the prices you calculated in parts a) and b). Further assume that any fraction of the bond can be bought or short sold - that is, if you buy (short sell) N bonds, then you would pay (receive) $35.50XN today and receive (pay) $36XN in 1 year for any real number N. Design an arbitrage strategy using the bond, stock, call, and put option, and show that the strategy has a zero cost with a sure profit at the end of Year 1. (4 marks) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.2 0.4207 0.4168 04129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.29120.2877 0.2843 0.2810 0.2776 -0.6 0.2743 0.2709 0.2676 0.2613 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.8 0.2119 0.2090 0_2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.17110.1683 0.1660 0.1635 0.1611 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.100.1020 0.1003 0.0985 0.0968 0.0951 0.0934 0.0918 0.0001 0.0885 0.0869 0.0853 0.0838 0.0823 -1.4 0.0508 0.0793 0.0778 0.0766 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.6 0.05.18 0.0837 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0165 0.0155 0.0446 0.0436 00427 0.048 0.0400 0.0401 0.0392 0.0384 0.0375 0.0367 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.025 0.0244 0.0239 0.0233 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.1 0.0179 0.0174 00170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.2. 0.0139 0.0136 0.0132 0.0129 0.0125 0.01220.0119 0.0116 0.0113 0.010 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0095 0.0091 0.0089 0.0087 0.0084 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -25 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.6 0.0047 0.0045 0.0014 0.0043 0.0041 0.0039 0.0038 0.0037 0.0036 2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0-0030 0.0029 0.0028 0.0027 0.0026 -2.8 0.0026 0.0025 0.0024 OLX23 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 2.9 0.0019 0.0018 0.0018 0.0017 0.8016 0.0016 0.0015 0.0015 0.0014 0.0014 3.0 0.0014 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.0010 0.0009 0.0009 0.0009 0.0008 0.0005 0.0008 O.CO 0.0007 0.0007 0.0007 0.0007 0.000 0.0006 0.0006 0.0006 OKOS D.ODOS 0.000s 0.0005 0.0005 0.0005 0.0004 0.0004 0.0001 0.0004 0.000 0.0003 0.0003 0.003 0.0003 00003 0.0003 0.0003 DO 0.0003 0.0003 0.0002 0.000Z 0.0002 0.0002 0.0002 0.000 0.02 0.0002 0.0002 0.0002 0.0002 00002 00002 0.0001 0.0001 0.000 0.0001 0.0001 0.0001 0.0001 0.0001 3.7 0.001 0.0001 0001 0.000 0.00 0.0001 0.0001 0.0001 0.0001 0.0001 38 0.0001 00001 0.0001 0.0001 0.0001 0.0001 0.0001 00001 0.0001 0.0001 0.0000 0.000 0.00 0.000 0.0000 0. 0.0000 0 0000 00000 0.000 0.0000 0.000 0.00 OOOXXO 0.0000 0.000 0.0000 0 0000 0.00