# Statistics-AW-Q422

## Statistics-AW-Q422 Online Services

what to turn in part 1 – Table with six volatility estimates (% per year)
what to turn in part 2 – 3 plots with B-Sch option prices for volatility estimates (i),(iv),(v)

part 1

0. Assume there are 252 trading days a year.

Use S&P 500 dataset for 2006.

1. Compute several volatility estimates –

(i) last quarter, (ii) last 2 quarters, (iii) last 3 quarters, (iv) whole year, (v) exponentially weighted moving average (EWMA) with w=0.94 and 60 last days, (vi) exponentially weighted moving average (EWMA) with w=0.94 and 200 last days.

Dataset for 2006: Format of the file =[Date] [Open] [High] [Low] [Close] [Volume] [Adjusted Close]
You need to use the Adjusted Close values to estimate volatility.

2006-12-29 1424.71 1427 1416.84 1418.3 1678200000 1418.3
2006-12-28 1426.77 1427.26 1422.05 1424.73 1508570000 1424.73
2006-12-27 1416.63 1427.72 1416.63 1426.84 1667370000 1426.84
2006-12-26 1410.75 1417.91 1410.45 1416.9 1310310000 1416.9
2006-12-22 1418.1 1418.82 1410.28 1410.76 1647590000 1410.76
2006-12-21 1423.2 1426.4 1415.9 1418.3 2322410000 1418.3
2006-12-20 1425.51 1429.05 1423.51 1423.53 2387630000 1423.53
2006-12-19 1422.42 1428.3 1414.88 1425.55 2717060000 1425.55
2006-12-18 1427.08 1431.81 1420.65 1422.48 2568140000 1422.48
2006-12-15 1425.48 1431.63 1425.48 1427.09 3229580000 1427.09
2006-12-14 1413.16 1427.23 1413.16 1425.49 2729700000 1425.49
2006-12-13 1411.32 1416.64 1411.05 1413.21 2552260000 1413.21
2006-12-12 1413 1413.78 1404.75 1411.56 2738170000 1411.56
2006-12-13 1411.32 1416.64 1411.05 1413.21 2552260000 1413.21
2006-12-12 1413 1413.78 1404.75 1411.56 2738170000 1411.56
2006-12-11 1409.81 1415.6 1408.56 1413.04 2289900000 1413.04
2006-12-08 1407.27 1414.09 1403.67 1409.84 2440460000 1409.84
2006-12-07 1412.86 1418.27 1406.8 1407.29 2743150000 1407.29
2006-12-06 1414.4 1415.93 1411.05 1412.9 2725280000 1412.9
2006-12-05 1409.1 1415.27 1408.78 1414.76 2755700000 1414.76
2006-12-04 1396.67 1411.23 1396.67 1409.12 2766320000 1409.12
2006-12-01 1400.63 1402.46 1385.93 1396.71 2800980000 1396.71
2006-11-30 1399.47 1406.3 1393.83 1400.63 4006230000 1400.63
2006-11-29 1386.11 1401.14 1386.11 1399.48 2790970000 1399.48
2006-11-28 1381.61 1387.91 1377.83 1386.72 2639750000 1386.72
2006-11-27 1400.95 1400.95 1381.44 1381.96 2711210000 1381.96
2006-11-24 1405.94 1405.94 1399.25 1400.95 832550000 1400.95
2006-11-22 1402.69 1407.89 1402.26 1406.09 2237710000 1406.09
2006-11-21 1400.43 1403.49 1399.99 1402.81 2597940000 1402.81
2006-11-20 1401.17 1404.37 1397.85 1400.5 2546710000 1400.5
2006-11-17 1399.76 1401.21 1394.55 1401.2 2726100000 1401.2
2006-11-16 1396.53 1403.76 1396.53 1399.76 2835730000 1399.76
2006-11-15 1392.91 1401.35 1392.13 1396.57 2831130000 1396.57
2006-11-14 1384.36 1394.49 1379.07 1393.22 3027480000 1393.22
2006-11-13 1380.58 1387.61 1378.8 1384.42 2386340000 1384.42
2006-11-10 1378.33 1381.04 1375.6 1380.9 2290200000 1380.9
2006-11-09 1385.43 1388.92 1377.31 1378.33 3012050000 1378.33
2006-11-08 1382.5 1388.61 1379.33 1385.72 2814820000 1385.72
2006-11-07 1379.75 1388.19 1379.19 1382.84 2636390000 1382.84
2006-11-06 1364.27 1381.4 1364.27 1379.78 2533550000 1379.78
2006-11-03 1367.31 1371.68 1360.98 1364.3 2419730000 1364.3
2006-11-02 1367.44 1368.39 1362.21 1367.34 2646180000 1367.34
2006-11-01 1377.76 1381.95 1366.26 1367.81 2821160000 1367.81
2006-10-31 1377.93 1381.21 1372.19 1377.94 2803030000 1377.94
2006-10-30 1377.3 1381.22 1373.46 1377.93 2770440000 1377.93
2006-10-27 1388.89 1388.89 1375.85 1377.34 2458450000 1377.34
2006-10-26 1382.21 1389.45 1379.47 1389.08 2793350000 1389.08
2006-10-25 1377.36 1383.61 1376 1382.22 2953540000 1382.22
2006-10-24 1377.02 1377.78 1372.42 1377.38 2876890000 1377.38
2006-10-23 1368.58 1377.4 1363.94 1377.02 2480430000 1377.02
2006-10-20 1366.94 1368.66 1362.1 1368.6 2526410000 1368.6
2006-10-19 1365.95 1368.09 1362.06 1366.96 2619830000 1366.96
2006-10-18 1363.93 1372.87 1360.95 1365.8 2658840000 1365.8
2006-10-17 1369.05 1369.05 1356.87 1364.05 2519620000 1364.05
2006-10-16 1365.61 1370.2 1364.48 1369.06 2305920000 1369.06
2006-10-13 1362.82 1366.63 1360.5 1365.62 2482920000 1365.62
2006-10-12 1349.94 1363.76 1349.94 1362.83 2514350000 1362.83
2006-10-11 1353.28 1353.97 1343.57 1349.95 2521000000 1349.95
2006-10-10 1350.62 1354.23 1348.6 1353.42 2376140000 1353.42
2006-10-09 1349.58 1352.69 1346.55 1350.66 1935170000 1350.66
2006-10-06 1353.22 1353.22 1344.21 1349.59 2523000000 1349.59
2006-10-05 1349.84 1353.79 1347.75 1353.22 2817240000 1353.22
2006-10-04 1333.81 1350.2 1331.48 1350.2 3019880000 1350.2
2006-10-03 1331.32 1338.31 1327.1 1334.11 2682690000 1334.11
2006-10-02 1335.82 1338.54 1330.28 1331.32 2154480000 1331.32
2006-09-29 1339.15 1339.88 1335.64 1335.85 2273430000 1335.85
2006-09-28 1336.56 1340.28 1333.75 1338.88 2397820000 1338.88
2006-09-27 1336.12 1340.08 1333.54 1336.59 2749190000 1336.59
2006-09-26 1326.35 1336.6 1325.3 1336.35 2673350000 1336.35
2006-09-25 1314.78 1329.35 1311.58 1326.37 2710240000 1326.37
2006-09-22 1318.03 1318.03 1310.94 1314.78 2162880000 1314.78
2006-09-21 1324.89 1328.19 1315.45 1318.03 2627440000 1318.03
2006-09-20 1318.28 1328.53 1318.28 1325.18 2543070000 1325.18
2006-09-19 1321.17 1322.04 1312.17 1317.64 2390850000 1317.64
2006-09-18 1319.85 1324.87 1318.16 1321.18 2325080000 1321.18
2006-09-15 1316.28 1324.65 1316.28 1319.66 3198030000 1319.66
2006-09-14 1318 1318 1313.25 1316.28 2351220000 1316.28
2006-09-13 1312.74 1319.92 1311.12 1318.07 2597220000 1318.07
2006-09-12 1299.53 1314.28 1299.53 1313 2791580000 1313
2006-09-11 1298.86 1302.36 1290.93 1299.54 2506430000 1299.54
2006-09-08 1294.02 1300.14 1294.02 1298.92 2132890000 1298.92
2006-09-07 1300.21 1301.25 1292.13 1294.02 2325850000 1294.02
2006-09-06 1313.04 1313.04 1299.28 1300.26 2329870000 1300.26
2006-09-05 1310.94 1314.67 1308.82 1313.25 2114480000 1313.25
2006-09-01 1303.8 1312.03 1303.8 1311.01 1800520000 1311.01
2006-08-31 1304.25 1306.11 1302.45 1303.82 1974540000 1303.82
2006-08-30 1303.7 1306.74 1302.15 1305.37 2060690000 1305.37
2006-08-29 1301.57 1305.02 1295.29 1304.28 2093720000 1304.28
2006-08-28 1295.09 1305.02 1293.97 1301.78 1834920000 1301.78
2006-08-25 1295.92 1298.88 1292.39 1295.09 1667580000 1295.09
2006-08-24 1292.97 1297.23 1291.4 1296.06 1930320000 1296.06
2006-08-23 1298.73 1301.5 1289.82 1292.99 1893670000 1292.99
2006-08-22 1297.52 1302.49 1294.44 1298.82 1908740000 1298.82
2006-08-21 1302.3 1302.3 1295.51 1297.52 1759240000 1297.52
2006-08-18 1297.48 1302.3 1293.57 1302.3 2033910000 1302.3
2006-08-17 1295.37 1300.78 1292.71 1297.48 2458340000 1297.48
2006-08-16 1285.27 1296.21 1285.27 1295.43 2554570000 1295.43
2006-08-15 1268.19 1286.23 1268.19 1285.58 2334100000 1285.58
2006-08-14 1266.67 1278.9 1266.67 1268.21 2118020000 1268.21
2006-08-11 1271.64 1271.64 1262.08 1266.74 2004540000 1266.74
2006-08-10 1265.72 1272.55 1261.3 1271.81 2402190000 1271.81
2006-08-09 1271.13 1283.74 1264.73 1265.95 2555180000 1265.95
2006-08-08 1275.67 1282.75 1268.37 1271.48 2457840000 1271.48
2006-08-07 1279.31 1279.31 1273 1275.77 2045660000 1275.77
2006-08-04 1280.26 1292.92 1273.82 1279.36 2530970000 1279.36
2006-08-03 1278.22 1283.96 1271.25 1280.27 2728440000 1280.27
2006-08-02 1270.73 1283.42 1270.73 1277.41 2610750000 1277.41
2006-08-01 1278.53 1278.66 1265.71 1270.92 2527690000 1270.92
2006-07-31 1278.53 1278.66 1274.31 1276.66 2461300000 1276.66
2006-07-28 1263.15 1280.42 1263.15 1278.55 2480420000 1278.55
2006-07-27 1268.2 1275.85 1261.92 1263.2 2776710000 1263.2
2006-07-26 1268.87 1273.89 1261.94 1268.4 2667710000 1268.4
2006-07-25 1260.91 1272.39 1257.19 1268.88 2563930000 1268.88
2006-07-24 1240.25 1262.5 1240.25 1260.91 2312720000 1260.91
2006-07-21 1249.12 1250.96 1238.72 1240.29 2704090000 1240.29
2006-07-20 1259.81 1262.56 1249.13 1249.13 2345580000 1249.13
2006-07-19 1236.74 1261.81 1236.74 1259.81 2701980000 1259.81
2006-07-18 1234.48 1239.86 1224.54 1236.86 2481750000 1236.86
2006-07-17 1236.2 1240.07 1231.49 1234.49 2146410000 1234.49
2006-07-14 1242.29 1242.7 1228.45 1236.2 2467120000 1236.2
2006-07-13 1258.58 1258.58 1241.43 1242.28 2545760000 1242.28
2006-07-12 1272.39 1273.31 1257.29 1258.6 2250450000 1258.6
2006-07-11 1267.26 1273.64 1259.65 1272.43 2310850000 1272.43
2006-07-10 1265.46 1274.06 1264.46 1267.34 1854590000 1267.34
2006-07-07 1274.08 1275.38 1263.13 1265.48 1988150000 1265.48
2006-07-06 1270.58 1278.32 1270.58 1274.08 2009160000 1274.08
2006-07-05 1280.05 1280.05 1265.91 1270.91 2165070000 1270.91
2006-07-03 1270.06 1280.38 1270.06 1280.19 1114470000 1280.19
2006-06-30 1272.86 1276.3 1270.2 1270.2 3049560000 1270.2
2006-06-29 1245.94 1272.88 1245.94 1272.87 2621250000 1272.87
2006-06-28 1238.99 1247.06 1237.59 1246 2085490000 1246
2006-06-27 1250.55 1253.37 1238.94 1239.2 2203130000 1239.2
2006-06-26 1244.5 1250.92 1243.68 1250.56 1878580000 1250.56
2006-06-23 1245.59 1253.13 1241.43 1244.5 2017270000 1244.5
2006-06-22 1251.92 1251.92 1241.53 1245.6 2148180000 1245.6
2006-06-21 1240.09 1257.96 1240.09 1252.2 2361230000 1252.2
2006-06-20 1240.12 1249.01 1238.87 1240.12 2232950000 1240.12
2006-06-19 1251.54 1255.93 1237.17 1240.13 2517200000 1240.13
2006-06-16 1256.16 1256.27 1246.33 1251.54 2783390000 1251.54
2006-06-15 1230.01 1258.64 1230.01 1256.16 2775480000 1256.16
2006-06-14 1223.66 1231.46 1219.29 1230.04 2667990000 1230.04
2006-06-13 1236.08 1243.37 1222.52 1223.69 3215770000 1223.69
2006-06-12 1252.27 1255.22 1236.43 1237.44 2247010000 1237.44
2006-06-09 1257.93 1262.58 1250.03 1252.3 2214000000 1252.3
2006-06-08 1256.08 1259.85 1235.18 1257.93 3543790000 1257.93
2006-06-07 1263.61 1272.47 1255.77 1256.15 2644170000 1256.15
2006-06-06 1265.23 1269.88 1254.46 1263.85 2697650000 1263.85
2006-06-05 1288.16 1288.16 1264.66 1265.29 2313470000 1265.29
2006-06-02 1285.71 1290.68 1280.22 1288.22 2295540000 1288.22
2006-06-01 1270.05 1285.71 1269.19 1285.71 2360160000 1285.71
2006-05-31 1259.38 1270.09 1259.38 1270.09 2692160000 1270.09
2006-05-30 1280.04 1280.04 1259.87 1259.87 2176190000 1259.87
2006-05-26 1272.71 1280.54 1272.5 1280.16 1814020000 1280.16
2006-05-25 1258.41 1273.26 1258.41 1272.88 2372730000 1272.88
2006-05-24 1256.56 1264.53 1245.34 1258.57 2999030000 1258.57
2006-05-23 1262.06 1273.67 1256.15 1256.58 2605250000 1256.58
2006-05-22 1267.03 1268.77 1252.98 1262.07 2773010000 1262.07
2006-05-19 1261.81 1272.15 1256.28 1267.03 2982300000 1267.03
2006-05-18 1270.25 1274.89 1261.75 1261.81 2537490000 1261.81
2006-05-17 1291.73 1291.73 1267.31 1270.32 2830200000 1270.32
2006-05-16 1294.5 1297.88 1288.51 1292.08 2386210000 1292.08
2006-05-15 1291.19 1294.81 1284.51 1294.5 2505660000 1294.5
2006-05-12 1305.88 1305.88 1290.38 1291.24 2567970000 1291.24
2006-05-11 1322.63 1322.63 1303.45 1305.92 2531520000 1305.92
2006-05-10 1324.57 1325.51 1317.44 1322.85 2268550000 1322.85
2006-05-09 1324.66 1326.6 1322.48 1325.14 2157290000 1325.14
2006-05-08 1325.76 1326.7 1322.87 1324.66 2151300000 1324.66
2006-05-05 1312.25 1326.53 1312.25 1325.76 2294760000 1325.76
2006-05-04 1307.85 1315.14 1307.85 1312.25 2431450000 1312.25
2006-05-03 1313.21 1313.47 1303.92 1308.12 2395230000 1308.12
2006-05-02 1305.19 1313.66 1305.19 1313.21 2403470000 1313.21
2006-05-01 1310.61 1317.21 1303.46 1305.19 2437040000 1305.19
2006-04-28 1309.72 1316.04 1306.16 1310.61 2419920000 1310.61
2006-04-27 1305.41 1315 1295.57 1309.72 2772010000 1309.72
2006-04-26 1301.74 1310.97 1301.74 1305.41 2502690000 1305.41
2006-04-25 1308.11 1310.79 1299.17 1301.74 2366380000 1301.74
2006-04-24 1311.28 1311.28 1303.79 1308.11 2117330000 1308.11
2006-04-21 1311.46 1317.67 1306.59 1311.28 2392630000 1311.28
2006-04-20 1309.93 1318.16 1306.38 1311.46 2512920000 1311.46
2006-04-19 1307.65 1310.39 1302.79 1309.93 2447310000 1309.93
2006-04-18 1285.33 1309.02 1285.33 1307.28 2595440000 1307.28
2006-04-17 1289.12 1292.45 1280.74 1285.33 1794650000 1285.33
2006-04-13 1288.12 1292.09 1283.37 1289.12 1891940000 1289.12
2006-04-12 1286.57 1290.93 1286.45 1288.12 1938100000 1288.12
2006-04-11 1296.6 1300.71 1282.96 1286.57 2232880000 1286.57
2006-04-10 1295.51 1300.74 1293.17 1296.62 1898320000 1296.62
2006-04-07 1309.04 1314.07 1294.18 1295.5 2082470000 1295.5
2006-04-06 1311.56 1311.99 1302.44 1309.04 2281680000 1309.04
2006-04-05 1305.93 1312.81 1304.82 1311.56 2420020000 1311.56
2006-04-04 1297.81 1307.55 1294.71 1305.93 2147660000 1305.93
2006-04-03 1302.88 1309.19 1296.65 1297.81 2494080000 1297.81
2006-03-31 1300.25 1303 1294.87 1294.87 2236710000 1294.87
2006-03-30 1302.89 1310.15 1296.72 1300.25 2294560000 1300.25
2006-03-29 1293.23 1305.6 1293.23 1302.89 2143540000 1302.89
2006-03-28 1301.61 1306.24 1291.84 1293.23 2148580000 1293.23
2006-03-27 1302.95 1303.74 1299.09 1301.61 2029700000 1301.61
2006-03-24 1301.67 1306.53 1298.89 1302.95 2326070000 1302.95
2006-03-23 1305.04 1305.04 1298.11 1301.67 1980940000 1301.67
2006-03-22 1297.23 1305.97 1295.81 1305.04 2039810000 1305.04
2006-03-21 1305.08 1310.88 1295.82 1297.23 2147370000 1297.23
2006-03-20 1307.25 1310 1303.59 1305.08 1976830000 1305.08
2006-03-17 1305.33 1309.79 1305.32 1307.25 2549620000 1307.25
2006-03-16 1303.02 1310.45 1303.02 1305.33 2292180000 1305.33
2006-03-15 1297.48 1304.4 1294.97 1303.02 2293000000 1303.02
2006-03-14 1284.13 1298.14 1282.67 1297.48 2165270000 1297.48
2006-03-13 1281.58 1287.37 1281.58 1284.13 2070330000 1284.13
2006-03-10 1272.23 1284.37 1271.11 1281.42 2123450000 1281.42
2006-03-09 1278.47 1282.74 1272.23 1272.23 2140110000 1272.23
2006-03-08 1275.88 1280.33 1268.42 1278.47 2442870000 1278.47
2006-03-07 1278.26 1278.26 1271.11 1275.88 2268050000 1275.88
2006-03-06 1287.23 1288.23 1275.67 1278.26 2280190000 1278.26
2006-03-03 1289.14 1297.33 1284.2 1287.23 2152950000 1287.23
2006-03-02 1291.24 1291.24 1283.21 1289.14 2494590000 1289.14
2006-03-01 1280.66 1291.8 1280.66 1291.24 2308320000 1291.24
2006-02-28 1294.12 1294.12 1278.66 1280.66 2370860000 1280.66
2006-02-27 1289.43 1297.57 1289.43 1294.12 1975320000 1294.12
2006-02-24 1287.79 1292.11 1285.62 1289.43 1933010000 1289.43
2006-02-23 1292.67 1293.84 1285.14 1287.79 2144210000 1287.79
2006-02-22 1283.03 1294.17 1283.03 1292.67 2222380000 1292.67
2006-02-21 1287.24 1291.92 1281.33 1283.03 2104320000 1283.03
2006-02-17 1289.38 1289.47 1284.07 1287.24 2128260000 1287.24
2006-02-16 1280 1289.39 1280 1289.38 2251490000 1289.38
2006-02-15 1275.53 1281 1271.06 1280 2317590000 1280
2006-02-14 1262.86 1278.21 1260.8 1275.53 2437940000 1275.53
2006-02-13 1266.99 1266.99 1258.34 1262.86 1850080000 1262.86
2006-02-10 1263.82 1269.89 1254.98 1266.99 2290050000 1266.99
2006-02-09 1265.65 1274.56 1262.8 1263.78 2441920000 1263.78
2006-02-08 1254.78 1266.47 1254.78 1265.65 2456860000 1265.65
2006-02-07 1265.02 1265.78 1253.61 1254.78 2366370000 1254.78
2006-02-06 1264.03 1267.04 1261.62 1265.02 2132360000 1265.02
2006-02-03 1270.84 1270.87 1261.02 1264.03 2282210000 1264.03
2006-02-02 1282.46 1282.46 1267.72 1270.84 2565300000 1270.84
2006-02-01 1280.08 1283.33 1277.57 1282.46 2589410000 1282.46
2006-01-31 1285.2 1285.2 1276.85 1280.08 2708310000 1280.08
2006-01-30 1283.72 1287.94 1283.51 1285.19 2282730000 1285.19
2006-01-27 1273.83 1286.38 1273.83 1283.72 2623620000 1283.72
2006-01-26 1264.68 1276.44 1264.68 1273.83 2856780000 1273.83
2006-01-25 1266.86 1271.87 1259.42 1264.68 2617060000 1264.68
2006-01-24 1263.82 1271.47 1263.82 1266.86 2608720000 1266.86
2006-01-23 1261.49 1268.19 1261.49 1263.82 2256070000 1263.82
2006-01-20 1285.04 1285.04 1260.92 1261.49 2845810000 1261.49
2006-01-19 1277.93 1287.79 1277.93 1285.04 2444020000 1285.04
2006-01-18 1282.93 1282.93 1272.08 1277.93 2233200000 1277.93
2006-01-17 1287.61 1287.61 1278.61 1283.03 2179970000 1283.03
2006-01-13 1286.06 1288.96 1282.78 1287.61 2206510000 1287.61
2006-01-12 1294.18 1294.18 1285.04 1286.06 2318350000 1286.06
2006-01-11 1289.72 1294.9 1288.12 1294.18 2406130000 1294.18
2006-01-10 1290.15 1290.15 1283.76 1289.69 2373080000 1289.69
2006-01-09 1285.45 1290.78 1284.82 1290.15 2301490000 1290.15
2006-01-06 1273.48 1286.09 1273.48 1285.45 2446560000 1285.45
2006-01-05 1273.46 1276.91 1270.3 1273.48 2433340000 1273.48
2006-01-04 1268.8 1275.37 1267.74 1273.46 2515330000 1273.46
2006-01-03 1248.29 1270.22 1245.74 1268.8 2554570000 1268.8

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## Related Services

Part 2

Assume that the trading day is 1/3/2007, S&P 500 = 1416.63.
Use r = 5% / year
Strike prices are given in the options dataset #1.

1. Use volatility estimates (i),(iv),(v) from part 1 to compute the BS option prices for the expiry date 2/17/2007.
2. Compare with the options dataset #1.
3. Plot Option Price with volatility estimates (i),(iv),(v) vs Strike Price. Each on a separate graph; make 3 plots.
Plot the observed option price on each graph as well.

Dataset #1

This dataset contains option prices (for different srike prices) for the S&P 500 Index on 1/3/2007.
All options have the expiry date 2/17/2007.
S&P 500 Index on 1/3/2007 = 1416.63.

Format of the file = [Strike Price] [Bid Price] [Ask Price]
1360 66.7 68.7
1365 62.4 64.4
1370 58.1 60.1
1375 54 56
1380 49.9 51.9
1385 45.9 47.9
1390 42 44
1395 38.2 40.2
1400 34.5 36.5
1405 31.1 33.1
1410 27.6 29.6
1415 24.4 26.4
1420 21.4 23.4
1425 19 20.3
1430 16 17.6
1435 13.6 15.2
1440 11.3 12.9
1445 9.6 10.6
1450 7.8 8.8
1455 6.2 7.2
1460 5 5.8
1465 3.8 4.6
1470 2.9 3.5

Product Code-Statistics-AW-Q422