11_18_2010 Black(1976)

11_18_2010 Black(1976) - days 91.25 182.5 365 T 0.25 0.5 1...

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days T Rate d(0,T) T d(0,T) 3 M FWD 91.25 0.25 0.28 0.9993 0.25 0.9993 182.5 0.5 0.44 0.9978 0.5 0.9978 0.00600 365 1 0.77 0.9923 0.75 0.9950 0.01093 1.5 0.72 0.9893 0.36 1 0.9923 0.01096 2 0.67 0.9867 0.335 1.25 0.9908 0.00593 2.5 0.82 0.9797 0.41 1.5 0.9893 0.00594 3 0.97 0.9713 0.485 1.75 0.9880 0.00511 3.5 1.15 0.9605 0.575 2 0.9867 0.00512 4 1.33 0.9480 0.665 2.25 0.9832 0.01403 4.5 1.52 0.9333 0.761 2.5 0.9797 0.01408 5 1.71 0.9171 0.857 2.75 0.9755 0.01703 5.5 1.89 0.9002 0.94375 3 0.9713 0.01710 6 2.06 0.8819 1.0305 3.25 0.9659 0.02215 6.5 2.21 0.8636 1.10675 3.5 0.9605 0.02228 7 2.37 0.8442 1.183 3.75 0.9542 0.02583 7.5 2.49 0.8256 1.2465 4 0.9480 0.02600 8 2.62 0.8062 1.31 4.25 0.9407 0.03065 8.5 2.72 0.7878 1.3615 4.5 0.9333 0.03089 9 2.83 0.7689 1.413 4.75 0.9252 0.03468 9.5 2.91 0.7508 1.457 5 0.9171 0.03499 10 3.00 0.7323 1.501 5.25 0.9086 0.03667 5.5 0.9002 0.03701 5.75 0.8911 0.04043 6 0.8819 0.04085
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Evaluation of 5 year CAP, according to Black Model Volatility 0.4828 Cap 3.23164 in dollars Strike 0.0176 323 in BP Notional 100 Caplet No Expiration T d(0,T) Fwd Vola Strike d1 d2 N(d1) N(d2) C 1 0.25 0.50 0.9978 0.00600 0.4828 0.0176 -4.340 -4.582 0.000 0.000 0.000 2 0.50 0.75 0.9950 0.01093 0.4828 0.0176 -1.226 -1.567 0.110 0.059 0.004 3 0.75 1.00 0.9923 0.01096 0.4828 0.0176 -0.925 -1.343 0.178 0.090 0.009 4 1.00 1.25 0.9908 0.00593 0.4828 0.0176 -2.011 -2.494 0.022 0.006 0.001 5 1.25 1.50 0.9893 0.00594 0.4828 0.0176 -1.742 -2.282 0.041 0.011 0.001 6 1.50 1.75 0.9880 0.00511 0.4828 0.0176 -1.795 -2.386 0.036 0.009 0.001 7 1.75 2.00 0.9867 0.00512 0.4828 0.0176 -1.614 -2.253 0.053 0.012 0.001 8 2.00 2.25 0.9832 0.01403 0.4828 0.0176 0.009 -0.674 0.504 0.250 0.066 9 2.25 2.50 0.9797 0.01408 0.4828 0.0176 0.054 -0.671 0.521 0.251 0.072 10 2.50 2.75 0.9755 0.01703 0.4828 0.0176 0.338 -0.425 0.632 0.335 0.120 11 2.75 3.00 0.9713 0.01710 0.4828 0.0176 0.364 -0.436 0.642 0.331 0.127 12 3.00 3.25 0.9659 0.02215 0.4828 0.0176 0.693 -0.143 0.756 0.443 0.219 13 3.25 3.50 0.9605 0.02228 0.4828 0.0176 0.706 -0.164 0.760 0.435 0.226
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This note was uploaded on 03/27/2012 for the course FNCE 235 taught by Professor Roussanov during the Spring '09 term at UPenn.

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11_18_2010 Black(1976) - days 91.25 182.5 365 T 0.25 0.5 1...

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