Range Resources stock sells for 120. The interest rate is 3 percent. The time to expiration is nine months on all call options. The standard deviation on Noble stock is 25 percent. The interest rate is 2 percent. You go short 140 call options at 125. A: (8 points): How do you delta hedge your portfolio? B: (12 points): You can also go long or short call options at 115. You will be happy to know that the delta on these options is 0.646, while the gamma is 0.01432. How do you delta- GAMMA hedge your position?

 

Normal Distribution Table N(X) 0.0122 -3 -1.5 -2.975 0.0015 -2.225 0.0130 -1.475 -2.95 0.0016 0.0139 -2.2 -2.925 0.0017 -2.175 0.0148 0.0019 -2.15 0.0158 -2.9 -2.875 0.0020 -2.125 0.0168 -2.85 0.0022 -2.1 0.0179 -2.825 0.0024 -2.075 0.0190 -2.8 0.0026 -2.05 0.0202 -2.775 0.0028 -2.025 0.0214 -2.75 0.0030 -2 0.0228 -2.725 0.0032 -1.975 0.0241 -2.7 0.0035 -1.95 0.0256 -2.675 0.0037 -1.925 0.0271 -2.65 0.0040 0.0287 -2.625 0.0043 -1.9 -1.875 0.0304 -1.125 -2.6 0.0047 -1.85 0.0322 -2.575 0.0050 -1.825 0.0340 -1.075 -1.1 -2.55 0.0054 0.0359 -1.05 -1.8 -2.525 0.0058 -1.775 0.0379 -1.025 -1.75 0.0401 -1 -2.5 0.0062 -2.475 0.0067 -1.725 0.0423 -0.975 -2.45 0.0071 -1.7 0.0446 -2.425 0.0077 -1.675 0.0470 -2.4 0.0082 -1.65 0.0495 -0.9 -2.375 0.0088 -1.625 0.0521 -0.875 -2.35 0.0094 -1.6 0.0548 -0.85 -2.325 0.0100 -1.575 0.0576 -0.825 -2.3 0.0107 -1.55 0.0606 -2.275 0.0115 -1.525 0.0636 X N(X) X 0.0013 -2.25 N(X) X 0.0668 -0.75 0.0701 -0.725 0.2342 -1.45 0.0735 -0.7 0.2420 -1.425 0.0771 -0.675 0.2498 -1.4 0.0808 -0.65 0.2578 -1.375 0.0846 -0.625 0.2660 -1.35 0.0885 -0.6 0.2743 -1.325 0.0926 -0.575 0.2826 -1.3 0.0968 -0.55 0.2912 -1.275 0.1012 -0.525 0.2998 -1.25 0.1056 -0.5 0.3085 -1.225 0.1103 -0.475 0.3174 -1.2 0.1151 -0.45 0.3264 -1.175 0.1200 -0.425 0.3354 -1.15 0.1251 -0.4 0.3446 0.1303 -0.375 0.3538 0.1357 -0.35 0.3632 0.1412 -0.325 0.3726 0.1469 -0.3 0.3821 0.1527 -0.275 0.3917 0.1587 -0.25 0.4013 0.1648 -0.225 0.4110 0.4207 0.4305 0.4404 0.4503 0.4602 0.4701 0.4801 0.4900 0.5000 X -0.2 -0.95 0.1711 -0.925 0.1775 -0.175 0.1841 -0.15 0.1908 -0.125 0.1977 -0.1 0.2047 -0.075 -0.8 0.2119 -0.05 -0.775 0.2192 -0.025 0.0000 N(X) 0.2266