Knowledge

Delta neutral

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1481: 1471: 1461: 1491: 1168: 2409: 350:, or others, may form a delta neutral portfolio using related options instead of the underlying. The portfolio's delta (assuming the same underlier) is then the sum of all the individual options' deltas. This method can also be used when the underlier is difficult to trade, for instance when an underlying 50:
as close to zero as possible. In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re-hedged too frequently.
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to determine how much of the underlier to buy or sell to create a hedged portfolio. However, when the change in the value of the underlier is not small, the second-order term,
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describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security. Such a
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of the portfolio. By adjusting the amount bought or sold on new positions, the portfolio delta can be made to sum to zero, and the portfolio is then delta neutral. See
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Delta measures the sensitivity of the value of an option to changes in the price of the underlying stock assuming all other variables remain unchanged.
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components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.
335:- i.e. establishing the required hedge - may be accomplished by buying or selling an amount of the underlier that corresponds to the 2292: 1982: 1045: 987: 418: 960: 2114: 302:
Therefore, if a position is delta neutral (or, instantaneously delta-hedged) its instantaneous change in value, for an
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and rebalancing of the underlier's position. Typically, this rebalancing is performed daily or weekly.
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In practice, maintaining a delta neutral portfolio requires continuous recalculation of the position's
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to changes in the value of the underlying, a portfolio that is delta neutral is effectively
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The existence of a delta neutral portfolio was shown as part of the original proof of the
507: 8: 2266: 2054: 1977: 1800: 1494: 1400: 1380: 1207: 1182: 888: 47: 28: 2317: 2302: 2271: 2256: 2223: 2089: 1880: 1845: 1608: 1573: 1536: 1405: 1350: 1262: 954: 736:{\displaystyle C(s+\epsilon \,)=C(s)+\epsilon \,C'(s)+{1/2}\,\epsilon ^{2}\,C''(s)+...} 243: 172: 121: 2322: 2312: 2251: 2238: 2213: 2099: 1885: 1681: 1128: 1104: 1088: 914: 2203: 2142: 2137: 2119: 2049: 1815: 1810: 1782: 1734: 1613: 1553: 1297: 1232: 895: 832: 548: 336: 311: 234: 43: 36: 32: 87:
The sensitivity of an option's value to a change in the underlying stock's price.
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and their corresponding underlying securities such that positive and negative
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of the value of an option, we get the change in the value of an option,
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A related term, delta hedging is the process of setting or keeping the
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Delta is clearly a function of S, however Delta is also a function of
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change in the value of the underlying security, will be zero; see
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For any small change in the underlier, we can ignore the
454:{\displaystyle S{\frac {\delta V}{\delta S}}\approx V} 253: 872: 851: 796: 755: 617: 587: 557: 510: 467: 421: 367: 251: 197: 175: 146: 124: 95: 73: 879: 858: 823: 782: 735: 600: 573: 516: 496: 453: 391: 276: 218: 181: 159: 130: 108: 79: 277:{\displaystyle {\tfrac {\partial V}{\partial S}}} 2426: 497:{\displaystyle k={\frac {\delta V}{\delta S}}} 54: 1521: 981: 581:, for a change in the value of the underlier 1465:Alternative investment management companies 1442:Standards Board for Alternative Investments 935:"Welcome quantprinciple.com - BlueHost.com" 189:The current value of the underlying stock. 167:The initial value of the underlying stock. 1528: 1514: 1490: 1346:Taxation of private equity and hedge funds 988: 974: 961:Theory & Application for Delta Hedging 354:is hard to borrow and therefore cannot be 876: 855: 820: 779: 703: 692: 658: 633: 594: 570: 327: 242:Mathematically, delta is represented as 2353:Power reverse dual-currency note (PRDC) 2293:Constant proportion portfolio insurance 58: 2427: 1535: 929: 927: 1509: 1046:fixed-income relative-value investing 969: 341:Rational pricing § Delta hedging 2288:Collateralized debt obligation (CDO) 924: 13: 873: 852: 817: 776: 511: 368: 264: 256: 74: 14: 2456: 948: 288:with respect to the price of the 138:The current value of the option. 116:The initial value of the option. 2407: 1489: 1480: 1479: 1470: 1469: 1460: 1459: 1166: 824:{\displaystyle C''(s)=\Gamma \,} 995: 783:{\displaystyle C'(s)=\Delta \,} 226:The (call) option value 2115:Year-on-year inflation-indexed 907: 811: 805: 770: 764: 718: 712: 673: 667: 649: 643: 634: 621: 595: 588: 567: 561: 361:For example, in the portfolio 213: 201: 1: 2125:Zero-coupon inflation-indexed 901: 601:{\displaystyle (\epsilon \,)} 1320:security characteristic line 403:, and the stock has a value 7: 2328:Foreign exchange derivative 1720:Callable bull/bear contract 1308:Capital asset pricing model 1027:Capital structure arbitrage 316:measures the exposure of a 55:Mathematical interpretation 16:Type of financial portfolio 10: 2461: 1110:Commodity trading advisors 399:, an option has the value 392:{\displaystyle \Pi =-V+kS} 232: 60: 2402: 2361: 2280: 2237: 2229:Stock market index future 2133: 2010: 1918: 1781: 1690: 1627: 1561: 1552: 1543: 1455: 1447:Managed Funds Association 1429: 1391:High-net-worth individual 1363: 1271: 1225: 1216: 1175: 1164: 1142: 1097: 1064: 1012: 1003: 887:, cannot be ignored: see 880:{\displaystyle \Gamma \,} 859:{\displaystyle \Delta \,} 542:Black-Scholes: Derivation 531: 2348:Mortgage-backed security 2343:Interest rate derivative 2318:Equity-linked note (ELN) 2303:Credit-linked note (CLN) 1284:Arbitrage pricing theory 504:means that the value of 2298:Contract for difference 1599:Risk-free interest rate 1396:Institutional investors 1289:Assets under management 1114:managed futures account 80:{\displaystyle \Delta } 2080:Forward Rate Agreement 1421:Sovereign wealth funds 1193:High-frequency trading 1042:Fixed income arbitrage 939:www.quantprinciple.com 881: 860: 825: 784: 737: 602: 575: 574:{\displaystyle C(s)\,} 518: 498: 455: 393: 278: 220: 219:{\displaystyle C(...)} 183: 161: 132: 110: 81: 2440:Derivatives (finance) 2308:Credit default option 1652:Employee stock option 1263:Structured securities 1079:Distressed securities 1051:Statistical arbitrage 1037:Equity market neutral 1032:Convertible arbitrage 882: 861: 845:and use the quantity 826: 785: 738: 603: 576: 519: 499: 456: 415:, then we can assume 394: 328:Creating the position 279: 221: 184: 162: 160:{\displaystyle S_{0}} 133: 111: 109:{\displaystyle V_{0}} 82: 2445:Mathematical finance 2262:Inflation derivative 2247:Commodity derivative 2219:Single-stock futures 2209:Normal backwardation 2199:Interest rate future 2040:Conditional variance 1546:Derivative (finance) 1381:Financial endowments 1326:Fundamental analysis 1074:Shareholder activism 1056:Volatility arbitrage 870: 849: 794: 753: 615: 585: 555: 517:{\displaystyle \Pi } 508: 465: 461:, therefore letting 419: 365: 299:and time to expiry. 249: 195: 173: 144: 122: 93: 71: 2414:Business portal 2267:Property derivative 1495:List of hedge funds 1485:Hedge fund managers 1401:Insurance companies 1386:Fund of hedge funds 1294:Black–Scholes model 1208:Proprietary trading 1183:Algorithmic trading 1150:Fund of hedge funds 889:Convexity (finance) 538:Black–Scholes model 290:underlying security 31:typically contains 2272:Weather derivative 2257:Freight derivative 2239:Exotic derivatives 2159:Commodities future 1846:Intermarket spread 1609:Synthetic position 1537:Derivatives market 1351:Technical analysis 957:, investopedia.com 877: 856: 821: 780: 733: 598: 571: 514: 494: 451: 389: 274: 272: 244:partial derivative 216: 179: 157: 128: 106: 77: 2435:Financial markets 2422: 2421: 2323:Equity derivative 2313:Credit derivative 2281:Other derivatives 2252:Energy derivative 2214:Perpetual futures 2095:Overnight indexed 2045:Constant maturity 2006: 2005: 1953:Finite difference 1886:Protective option 1503: 1502: 1359: 1358: 1162: 1161: 1129:Long/short equity 1105:Convergence trade 1089:Special situation 843:second-order term 524:is approximately 492: 443: 271: 231: 230: 182:{\displaystyle S} 131:{\displaystyle V} 2452: 2412: 2411: 2184:Forwards pricing 1958:Garman–Kohlhagen 1559: 1558: 1530: 1523: 1516: 1507: 1506: 1493: 1492: 1483: 1482: 1473: 1472: 1463: 1462: 1406:Investment banks 1253:Foreign exchange 1223: 1222: 1170: 1010: 1009: 990: 983: 976: 967: 966: 943: 942: 931: 922: 911: 886: 884: 883: 878: 865: 863: 862: 857: 833:Greeks (finance) 830: 828: 827: 822: 804: 789: 787: 786: 781: 763: 742: 740: 739: 734: 711: 702: 701: 691: 687: 666: 607: 605: 604: 599: 580: 578: 577: 572: 549:Taylor expansion 523: 521: 520: 515: 503: 501: 500: 495: 493: 491: 483: 475: 460: 458: 457: 452: 444: 442: 434: 426: 398: 396: 395: 390: 284:of the option's 283: 281: 280: 275: 273: 270: 262: 254: 235:Greeks (finance) 225: 223: 222: 217: 188: 186: 185: 180: 166: 164: 163: 158: 156: 155: 137: 135: 134: 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If we assume 366: 363: 362: 330: 308:Hedge (finance) 263: 255: 252: 250: 247: 246: 237: 196: 193: 192: 174: 171: 170: 151: 147: 145: 142: 141: 123: 120: 119: 100: 96: 94: 91: 90: 72: 69: 68: 57: 17: 12: 11: 5: 2458: 2448: 2447: 2442: 2437: 2420: 2419: 2417: 2416: 2403: 2400: 2399: 2397: 2396: 2391: 2389:Municipal debt 2386: 2381: 2376: 2374:Corporate debt 2371: 2365: 2363: 2359: 2358: 2356: 2355: 2350: 2345: 2340: 2335: 2330: 2325: 2320: 2315: 2310: 2305: 2300: 2295: 2290: 2284: 2282: 2278: 2277: 2275: 2274: 2269: 2264: 2259: 2254: 2249: 2243: 2241: 2235: 2234: 2232: 2231: 2226: 2221: 2216: 2211: 2206: 2201: 2196: 2191: 2186: 2181: 2176: 2174:Forward market 2171: 2166: 2161: 2156: 2150: 2148: 2146: 2145: 2140: 2134: 2131: 2130: 2128: 2127: 2122: 2117: 2112: 2107: 2102: 2097: 2092: 2087: 2082: 2077: 2072: 2067: 2062: 2057: 2055:Credit default 2052: 2047: 2042: 2037: 2032: 2027: 2022: 2016: 2014: 2008: 2007: 2004: 2003: 2001: 2000: 1995: 1990: 1985: 1980: 1975: 1970: 1965: 1960: 1955: 1950: 1940: 1935: 1930: 1924: 1922: 1916: 1915: 1913: 1912: 1898: 1893: 1888: 1883: 1878: 1873: 1868: 1863: 1858: 1853: 1851:Iron butterfly 1848: 1843: 1838: 1833: 1828: 1823: 1821:Covered option 1818: 1813: 1808: 1803: 1798: 1793: 1787: 1785: 1779: 1778: 1776: 1775: 1770: 1765: 1760: 1759:Mountain range 1757: 1752: 1747: 1742: 1737: 1732: 1727: 1722: 1717: 1712: 1707: 1702: 1696: 1694: 1688: 1687: 1685: 1684: 1679: 1674: 1669: 1664: 1659: 1654: 1649: 1644: 1639: 1633: 1631: 1625: 1624: 1622: 1621: 1616: 1611: 1606: 1601: 1596: 1591: 1586: 1581: 1576: 1571: 1565: 1563: 1556: 1550: 1549: 1544: 1541: 1540: 1533: 1532: 1525: 1518: 1510: 1501: 1500: 1498: 1497: 1487: 1477: 1467: 1456: 1453: 1452: 1450: 1449: 1444: 1439: 1433: 1431: 1427: 1426: 1424: 1423: 1418: 1413: 1411:Merchant banks 1408: 1403: 1398: 1393: 1388: 1383: 1378: 1376:Family offices 1373: 1367: 1365: 1361: 1360: 1357: 1356: 1354: 1353: 1348: 1343: 1338: 1336:Securitization 1333: 1328: 1323: 1305: 1291: 1286: 1281: 1275: 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261: 258: 233:Main article: 229: 228: 215: 212: 209: 206: 203: 200: 178: 154: 150: 127: 103: 99: 76: 56: 53: 15: 9: 6: 4: 3: 2: 2457: 2446: 2443: 2441: 2438: 2436: 2433: 2432: 2430: 2415: 2410: 2405: 2404: 2401: 2395: 2392: 2390: 2387: 2385: 2382: 2380: 2377: 2375: 2372: 2370: 2369:Consumer debt 2367: 2366: 2364: 2362:Market issues 2360: 2354: 2351: 2349: 2346: 2344: 2341: 2339: 2338:Fund of funds 2336: 2334: 2331: 2329: 2326: 2324: 2321: 2319: 2316: 2314: 2311: 2309: 2306: 2304: 2301: 2299: 2296: 2294: 2291: 2289: 2286: 2285: 2283: 2279: 2273: 2270: 2268: 2265: 2263: 2260: 2258: 2255: 2253: 2250: 2248: 2245: 2244: 2242: 2240: 2236: 2230: 2227: 2225: 2222: 2220: 2217: 2215: 2212: 2210: 2207: 2205: 2202: 2200: 2197: 2195: 2192: 2190: 2187: 2185: 2182: 2180: 2179:Forward price 2177: 2175: 2172: 2170: 2167: 2165: 2162: 2160: 2157: 2155: 2152: 2151: 2149: 2144: 2141: 2139: 2136: 2135: 2132: 2126: 2123: 2121: 2118: 2116: 2113: 2111: 2108: 2106: 2103: 2101: 2098: 2096: 2093: 2091: 2090:Interest rate 2088: 2086: 2083: 2081: 2078: 2076: 2073: 2071: 2068: 2066: 2063: 2061: 2058: 2056: 2053: 2051: 2048: 2046: 2043: 2041: 2038: 2036: 2033: 2031: 2028: 2026: 2023: 2021: 2018: 2017: 2015: 2013: 2009: 1999: 1996: 1994: 1991: 1989: 1986: 1984: 1983:MC Simulation 1981: 1979: 1976: 1974: 1971: 1969: 1966: 1964: 1961: 1959: 1956: 1954: 1951: 1948: 1944: 1943:Black–Scholes 1941: 1939: 1936: 1934: 1931: 1929: 1926: 1925: 1923: 1921: 1917: 1910: 1906: 1902: 1899: 1897: 1896:Risk reversal 1894: 1892: 1889: 1887: 1884: 1882: 1879: 1877: 1874: 1872: 1869: 1867: 1864: 1862: 1859: 1857: 1854: 1852: 1849: 1847: 1844: 1842: 1839: 1837: 1834: 1832: 1829: 1827: 1826:Credit spread 1824: 1822: 1819: 1817: 1814: 1812: 1809: 1807: 1804: 1802: 1799: 1797: 1794: 1792: 1789: 1788: 1786: 1784: 1780: 1774: 1771: 1769: 1766: 1764: 1761: 1758: 1756: 1753: 1751: 1750:Interest rate 1748: 1746: 1745:Forward start 1743: 1741: 1738: 1736: 1733: 1731: 1728: 1726: 1723: 1721: 1718: 1716: 1713: 1711: 1708: 1706: 1703: 1701: 1698: 1697: 1695: 1693: 1689: 1683: 1680: 1678: 1675: 1673: 1672:Option styles 1670: 1668: 1665: 1663: 1660: 1658: 1655: 1653: 1650: 1648: 1645: 1643: 1640: 1638: 1635: 1634: 1632: 1630: 1626: 1620: 1617: 1615: 1612: 1610: 1607: 1605: 1602: 1600: 1597: 1595: 1592: 1590: 1589:Open interest 1587: 1585: 1582: 1580: 1577: 1575: 1572: 1570: 1569:Delta neutral 1567: 1566: 1564: 1560: 1557: 1555: 1551: 1547: 1542: 1538: 1531: 1526: 1524: 1519: 1517: 1512: 1511: 1508: 1496: 1488: 1486: 1478: 1476: 1468: 1466: 1458: 1457: 1454: 1448: 1445: 1443: 1440: 1438: 1435: 1434: 1432: 1428: 1422: 1419: 1417: 1416:Pension funds 1414: 1412: 1409: 1407: 1404: 1402: 1399: 1397: 1394: 1392: 1389: 1387: 1384: 1382: 1379: 1377: 1374: 1372: 1371:Vulture funds 1369: 1368: 1366: 1362: 1352: 1349: 1347: 1344: 1342: 1339: 1337: 1334: 1332: 1329: 1327: 1324: 1321: 1317: 1313: 1309: 1306: 1303: 1302:delta neutral 1299: 1295: 1292: 1290: 1287: 1285: 1282: 1280: 1277: 1276: 1274: 1270: 1264: 1261: 1259: 1258:Money markets 1256: 1254: 1251: 1249: 1246: 1244: 1241: 1239: 1236: 1234: 1231: 1230: 1228: 1224: 1221: 1215: 1209: 1206: 1204: 1201: 1199: 1196: 1194: 1191: 1189: 1186: 1184: 1181: 1180: 1178: 1174: 1169: 1155: 1154:Multi-manager 1151: 1148: 1147: 1145: 1141: 1135: 1132: 1130: 1127: 1125: 1122: 1120: 1117: 1115: 1111: 1108: 1106: 1103: 1102: 1100: 1096: 1090: 1087: 1085: 1082: 1080: 1077: 1075: 1072: 1071: 1069: 1067: 1063: 1057: 1054: 1052: 1049: 1047: 1043: 1040: 1038: 1035: 1033: 1030: 1028: 1025: 1024: 1022: 1020: 1015: 1011: 1008: 1002: 998: 991: 986: 984: 979: 977: 972: 971: 968: 962: 959: 956: 955:Delta Hedging 953: 952: 940: 936: 930: 928: 920: 919:0-470-02970-6 916: 913:De Weert F. 910: 906: 899: 897: 892: 890: 844: 834: 831:(gamma); see 814: 808: 801: 798: 773: 767: 760: 757: 748: 747: 746: 745: 730: 727: 724: 721: 715: 708: 705: 698: 694: 688: 684: 680: 676: 670: 663: 660: 655: 652: 646: 640: 637: 630: 627: 624: 618: 611: 610: 609: 591: 564: 558: 550: 545: 543: 539: 529: 527: 488: 485: 480: 477: 471: 468: 448: 445: 439: 436: 431: 428: 422: 414: 410: 406: 402: 386: 383: 380: 377: 374: 371: 359: 357: 353: 349: 348:market makers 344: 342: 338: 334: 333:Delta hedging 325: 323: 319: 315: 314: 309: 305: 304:infinitesimal 300: 298: 293: 291: 287: 267: 259: 245: 240: 236: 227: 210: 207: 204: 198: 190: 176: 168: 152: 148: 139: 125: 117: 101: 97: 88: 66: 65: 64:Nomenclature: 61: 52: 49: 45: 40: 38: 34: 30: 26: 25:delta neutral 22: 2189:Forward rate 2100:Total return 1988:Real options 1891:Ratio spread 1871:Naked option 1831:Debit spread 1662:Fixed income 1604:Strike price 1568: 1301: 1248:Fixed income 1124:Global macro 1066:Event-driven 938: 909: 893: 840: 790:(delta) and 546: 535: 525: 408: 404: 400: 360: 345: 332: 331: 312: 301: 297:strike price 294: 241: 238: 191: 169: 140: 118: 89: 67: 63: 62: 41: 24: 18: 2120:Zero Coupon 2050:Correlation 1998:Vanna–Volga 1856:Iron condor 1642:Bond option 1475:Hedge funds 1238:Derivatives 1233:Commodities 1188:Day trading 1098:Directional 997:Hedge funds 2429:Categories 2394:Tax policy 2110:Volatility 2020:Amortising 1861:Jelly roll 1796:Box spread 1791:Backspread 1783:Strategies 1619:Volatility 1614:the Greeks 1579:Expiration 1430:Governance 1004:Investment 902:References 356:sold short 318:derivative 286:fair value 2085:Inflation 2035:Commodity 1993:Trinomial 1928:Bachelier 1920:Valuation 1801:Butterfly 1735:Commodore 1584:Moneyness 1364:Investors 1014:Arbitrage 921:pp. 74-81 874:Γ 853:Δ 818:Γ 777:Δ 695:ϵ 656:ϵ 631:ϵ 592:ϵ 547:From the 512:Π 486:δ 478:δ 446:≈ 437:δ 429:δ 375:− 369:Π 265:∂ 257:∂ 75:Δ 48:portfolio 29:portfolio 2224:Slippage 2154:Contango 2138:Forwards 2105:Variance 2065:Dividend 2060:Currency 1973:Margrabe 1968:Lattices 1947:equation 1933:Binomial 1881:Strangle 1876:Straddle 1773:Swaption 1755:Lookback 1740:Compound 1682:Warrants 1657:European 1637:American 1629:Vanillas 1594:Pin risk 1574:Exercise 1006:strategy 802:″ 761:′ 709:″ 664:′ 346:Options 310:. Since 2143:Futures 1763:Rainbow 1730:Cliquet 1725:Chooser 1705:Barrier 1692:Exotics 1554:Options 1226:Markets 1217:Related 1176:Trading 33:options 21:finance 2204:Margin 2070:Equity 1963:Heston 1866:Ladder 1816:Condor 1811:Collar 1768:Spread 1715:Binary 1710:Basket 1298:Greeks 1243:Equity 917:  896:Greeks 749:where 532:Theory 413:linear 322:hedged 2075:Forex 2030:Basis 2025:Asset 2012:Swaps 1938:Black 1841:Fence 1700:Asian 1562:Terms 1341:Short 1331:Hedge 1312:alpha 1219:terms 1143:Other 352:stock 337:delta 313:delta 46:of a 44:delta 37:delta 1909:Bull 1905:Bear 1647:Call 1316:beta 1272:Misc 915:ISBN 1677:Put 411:is 19:In 2431:: 1907:, 1667:FX 1318:/ 1314:/ 1300:: 1152:/ 1112:/ 1044:/ 937:. 926:^ 891:. 608:: 544:. 528:. 358:. 343:. 292:. 23:, 1949:) 1945:( 1911:) 1903:( 1529:e 1522:t 1515:v 1322:) 1310:( 1304:) 1296:( 1016:/ 989:e 982:t 975:v 941:. 835:. 815:= 812:) 809:s 806:( 799:C 774:= 771:) 768:s 765:( 758:C 731:. 728:. 725:. 722:+ 719:) 716:s 713:( 706:C 699:2 689:2 685:/ 681:1 677:+ 674:) 671:s 668:( 661:C 653:+ 650:) 647:s 644:( 641:C 638:= 635:) 628:+ 625:s 622:( 619:C 596:) 589:( 568:) 565:s 562:( 559:C 526:0 489:S 481:V 472:= 469:k 449:V 440:S 432:V 423:S 409:V 405:S 401:V 387:S 384:k 381:+ 378:V 372:= 268:S 260:V 214:) 211:. 208:. 205:. 202:( 199:C 177:S 153:0 149:S 126:V 102:0 98:V

Index

finance
portfolio
options
delta
delta
portfolio
Greeks (finance)
partial derivative
fair value
underlying security
strike price
infinitesimal
Hedge (finance)
delta
derivative
hedged
delta
Rational pricing § Delta hedging
market makers
stock
sold short
linear
Black–Scholes model
Black-Scholes: Derivation
Taylor expansion
Greeks (finance)
second-order term
Convexity (finance)
Greeks
ISBN

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