3. (25 points) The generalized Black-Scholes/Merton model assumes that the under- lying asset price has a log-normal distribution. This implies that continuous re- turn, rt = ln(St/St1), is normally distributed with mean and standard deviation . Download daily stock price data for Samsung Electronics (005930.KS), Hyundai Motor(005380.KS), SK Hynix(000660.KS), Korea Electronic Power(015760.KS), and POSCO(005490.KS) for the calendar year beginning Dec 30, 2010 through Dec 31,2014. Use data form Yahoo finance (finance.yahoo.com). Compute the continuous returns for each price series, and then test the hypothesis that the return distribution is normal using the Jarque-Berra statistic. Plot a frequency distribution for each series to confirm what the test results show.

for references

Asset Price Volatility Rate Dividend Rate 80.00 25.00% 2.00% Step Time Incrementu 0.2500 1.1331 0.1875 1.1143 d 0.8825 0.8974 0.4988 0.4990 Call Option Exercise Price Time to expiratio 80.00 0.750 Interest Rate 5.00% BSM Value 7.6310 3 Steps t=0 t= 1 t =2 t=3 Asset price novements 116. 399 102.722 90.652 90.652 80.000 80.000 70.600 70.600 62. 304 54.983 t=0 t= 1 t =2 t=3 Call Option Valuation 36. 399 23. 203 14.028 10.652 8.190 5. 247 2. 585 0.000 0.000 0.000 t=4 t=0 t=3 t=1 t=2 t=3 Asset price novements t=1 t=2 t=3 Call Option Valuation 123. 352 43.352 110.696 31. 028 99.338 99.338 20.082 19.338 4 Steps 89. 146 89.146 12.272 9.559 80.000 80.000 80.000 7.226 4.725 0.000 71. 792 71. 792 2. 336 0.000 64. 426 64. 426 0.000 0.000 57. 816 0.000 51. 884 0.000 Asset Price Volatility Rate Dividend Rate 80.00 25.00% 2.00% Step Time Incrementu 0.2500 1.1331 0.1875 1.1143 d 0.8825 0.8974 0.4988 0.4990 Call Option Exercise Price Time to expiratio 80.00 0.750 Interest Rate 5.00% BSM Value 7.6310 3 Steps t=0 t= 1 t =2 t=3 Asset price novements 116. 399 102.722 90.652 90.652 80.000 80.000 70.600 70.600 62. 304 54.983 t=0 t= 1 t =2 t=3 Call Option Valuation 36. 399 23. 203 14.028 10.652 8.190 5. 247 2. 585 0.000 0.000 0.000 t=4 t=0 t=3 t=1 t=2 t=3 Asset price novements t=1 t=2 t=3 Call Option Valuation 123. 352 43.352 110.696 31. 028 99.338 99.338 20.082 19.338 4 Steps 89. 146 89.146 12.272 9.559 80.000 80.000 80.000 7.226 4.725 0.000 71. 792 71. 792 2. 336 0.000 64. 426 64. 426 0.000 0.000 57. 816 0.000 51. 884 0.000