Question

1. You own one call option and one put option on BP, both with a strike price of 230.   The price of BP is 226.   The interest rate is 3% and the time to expiration is six months. Graph on the same graph the value of the call and the put as the standard deviation of the price of Shell goes from 10 to 60 percent.     (So that is two lines on the same graph.)

Please include excel table and graph, with at least 50 data points (for example: 10,11,12,13,14,15, etc...), along with their formulas and detailed explanations of each step. Thank you.

Answer 1

Standard deviation	d1	d2	N(d1)	N(d2)	N(-d1)	N(-d2)	Call price	Put price
10%	-0.001	-0.071	0.500	0.472	0.500	0.528	6.098	6.674
11%	0.006	-0.072	0.502	0.471	0.498	0.529	6.736	7.312
12%	0.012	-0.072	0.505	0.471	0.495	0.529	7.373	7.949
13%	0.018	-0.074	0.507	0.471	0.493	0.529	8.011	8.587
14%	0.024	-0.075	0.509	0.470	0.491	0.530	8.648	9.224
15%	0.029	-0.077	0.512	0.469	0.488	0.531	9.286	9.861
16%	0.034	-0.079	0.514	0.468	0.486	0.532	9.923	10.499
17%	0.039	-0.081	0.516	0.468	0.484	0.532	10.560	11.136
18%	0.044	-0.084	0.517	0.467	0.483	0.533	11.197	11.773
19%	0.048	-0.086	0.519	0.466	0.481	0.534	11.834	12.410
20%	0.053	-0.089	0.521	0.465	0.479	0.535	12.470	13.046
21%	0.057	-0.091	0.523	0.464	0.477	0.536	13.107	13.683
22%	0.061	-0.094	0.524	0.463	0.476	0.537	13.743	14.319
23%	0.066	-0.097	0.526	0.461	0.474	0.539	14.380	14.955
24%	0.070	-0.100	0.528	0.460	0.472	0.540	15.016	15.592
25%	0.074	-0.103	0.529	0.459	0.471	0.541	15.652	16.227
26%	0.078	-0.106	0.531	0.458	0.469	0.542	16.287	16.863
27%	0.082	-0.109	0.533	0.457	0.467	0.543	16.923	17.499
28%	0.086	-0.112	0.534	0.455	0.466	0.545	17.558	18.134
29%	0.090	-0.115	0.536	0.454	0.464	0.546	18.193	18.769
30%	0.094	-0.118	0.537	0.453	0.463	0.547	18.828	19.404
31%	0.098	-0.121	0.539	0.452	0.461	0.548	19.463	20.038
32%	0.102	-0.124	0.541	0.451	0.459	0.549	20.097	20.673
33%	0.106	-0.128	0.542	0.449	0.458	0.551	20.731	21.307
34%	0.110	-0.131	0.544	0.448	0.456	0.552	21.365	21.941
35%	0.113	-0.134	0.545	0.447	0.455	0.553	21.999	22.574
36%	0.117	-0.137	0.547	0.445	0.453	0.555	22.632	23.208
37%	0.121	-0.141	0.548	0.444	0.452	0.556	23.265	23.841
38%	0.125	-0.144	0.550	0.443	0.450	0.557	23.898	24.473
39%	0.129	-0.147	0.551	0.442	0.449	0.558	24.530	25.106
40%	0.132	-0.150	0.553	0.440	0.447	0.560	25.162	25.738
41%	0.136	-0.154	0.554	0.439	0.446	0.561	25.794	26.370
42%	0.140	-0.157	0.556	0.438	0.444	0.562	26.425	27.001
43%	0.144	-0.160	0.557	0.436	0.443	0.564	27.057	27.632
44%	0.147	-0.164	0.559	0.435	0.441	0.565	27.687	28.263
45%	0.151	-0.167	0.560	0.434	0.440	0.566	28.318	28.894
46%	0.155	-0.170	0.562	0.432	0.438	0.568	28.948	29.524
47%	0.159	-0.174	0.563	0.431	0.437	0.569	29.578	30.154
48%	0.162	-0.177	0.564	0.430	0.436	0.570	30.207	30.783
49%	0.166	-0.181	0.566	0.428	0.434	0.572	30.836	31.412
50%	0.170	-0.184	0.567	0.427	0.433	0.573	31.465	32.041
51%	0.173	-0.187	0.569	0.426	0.431	0.574	32.093	32.669
52%	0.177	-0.191	0.570	0.424	0.430	0.576	32.721	33.297
53%	0.181	-0.194	0.572	0.423	0.428	0.577	33.348	33.924
54%	0.184	-0.198	0.573	0.422	0.427	0.578	33.975	34.551
55%	0.188	-0.201	0.575	0.420	0.425	0.580	34.602	35.178
56%	0.192	-0.204	0.576	0.419	0.424	0.581	35.228	35.804
57%	0.195	-0.208	0.577	0.418	0.423	0.582	35.854	36.430
58%	0.199	-0.211	0.579	0.416	0.421	0.584	36.479	37.055
59%	0.202	-0.215	0.580	0.415	0.420	0.585	37.104	37.680
60%	0.206	-0.218	0.582	0.414	0.418	0.586	37.728	38.304

Standard deviation	Call price	Put price
10%	6.098	6.674
11%	6.736	7.312
12%	7.373	7.949
13%	8.011	8.587
14%	8.648	9.224
15%	9.286	9.861
16%	9.923	10.499
17%	10.560	11.136
18%	11.197	11.773
19%	11.834	12.410
20%	12.470	13.046
21%	13.107	13.683
22%	13.743	14.319
23%	14.380	14.955
24%	15.016	15.592
25%	15.652	16.227
26%	16.287	16.863
27%	16.923	17.499
28%	17.558	18.134
29%	18.193	18.769
30%	18.828	19.404
31%	19.463	20.038
32%	20.097	20.673
33%	20.731	21.307
34%	21.365	21.941
35%	21.999	22.574
36%	22.632	23.208
37%	23.265	23.841
38%	23.898	24.473
39%	24.530	25.106
40%	25.162	25.738
41%	25.794	26.370
42%	26.425	27.001
43%	27.057	27.632
44%	27.687	28.263
45%	28.318	28.894
46%	28.948	29.524
47%	29.578	30.154
48%	30.207	30.783
49%	30.836	31.412
50%	31.465	32.041
51%	32.093	32.669
52%	32.721	33.297
53%	33.348	33.924
54%	33.975	34.551
55%	34.602	35.178
56%	35.228	35.804
57%	35.854	36.430
58%	36.479	37.055
59%	37.104	37.680
60%	37.728	38.304