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.
741:
459:
282:
502:
829:
788:
866:
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,
27:
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
606:
397:
339:
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
885:
864:
85:
579:
224:
165:
114:
522:
187:
136:
2246:
614:
2158:
1464:
239:
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.
1952:
1527:
1441:
934:
1957:
1345:
39:
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
248:
1850:
918:
464:
2352:
1520:
2439:
2287:
1932:
842:
2444:
541:
1484:
1319:
324:. That is, its overall value will not change for small changes in the price of its underlying instrument.
2327:
1865:
1719:
1513:
1307:
2434:
2183:
2124:
1946:
1018:
898:
and rebalancing of the underlier's position. Typically, this rebalancing is performed daily or weekly.
894:
In practice, maintaining a delta neutral portfolio requires continuous recalculation of the position's
793:
2228:
2039:
1446:
1390:
1109:
1036:
980:
752:
2347:
2342:
1283:
1153:
584:
2297:
1997:
1967:
1942:
1825:
1666:
1598:
1385:
1293:
1288:
1252:
1149:
1113:
537:
340:
364:
2094:
2079:
2044:
1987:
1395:
1192:
1065:
1041:
1026:
869:
848:
2307:
2074:
1972:
1651:
1420:
1078:
1050:
1031:
70:
554:
320:
to changes in the value of the underlying, a portfolio that is delta neutral is effectively
194:
2261:
2218:
2208:
2198:
2193:
1919:
1860:
1795:
1749:
1744:
1618:
1578:
1545:
1474:
1325:
1237:
1073:
1055:
973:
540:, the first comprehensive model to produce correct prices for some classes of options. See
317:
143:
92:
536:
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.
2413:
2383:
2378:
2332:
2168:
2163:
2109:
2019:
1927:
1900:
1840:
1835:
1805:
1754:
1739:
1656:
1636:
1436:
1340:
1330:
1311:
1278:
1202:
1197:
1133:
1118:
321:
307:
2388:
2373:
2173:
2084:
2034:
2011:
1992:
1820:
1762:
1729:
1724:
1704:
1628:
1335:
1315:
1083:
35:
and their corresponding underlying securities such that positive and negative
2428:
2368:
2337:
2178:
2104:
2064:
2059:
1895:
1767:
1714:
1709:
1691:
1588:
1410:
1375:
355:
303:
2188:
1962:
1890:
1870:
1830:
1699:
1671:
1661:
1603:
1415:
1370:
1257:
1242:
1123:
347:
296:
2069:
1937:
1908:
1904:
1855:
1646:
1641:
1247:
1187:
551:
of the value of an option, we get the change in the value of an option,
2393:
2029:
2024:
1790:
1676:
996:
289:
285:
42:
A related term, delta hedging is the process of setting or keeping the
295:
Delta is clearly a function of S, however Delta is also a function of
1583:
1505:
1013:
1167:
2153:
1875:
1772:
1593:
306:
change in the value of the underlying security, will be zero; see
20:
2408:
412:
965:
351:
841:
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:
129:
115:
113:
112:
107:
105:
104:
86:
84:
83:
78:
59:
2460:
2459:
2455:
2454:
2453:
2451:
2450:
2449:
2425:
2424:
2423:
2418:
2406:
2398:
2384:Great Recession
2379:Government debt
2357:
2333:Fund derivative
2276:
2233:
2194:Futures pricing
2169:Dividend future
2164:Currency future
2147:
2129:
2002:
1978:Put–call parity
1914:
1901:Vertical spread
1836:Diagonal spread
1806:Calendar spread
1777:
1686:
1623:
1548:
1539:
1534:
1504:
1499:
1451:
1437:Fund governance
1425:
1355:
1279:Absolute return
1267:
1218:
1212:
1203:Program trading
1198:Prime brokerage
1171:
1158:
1138:
1134:Trend following
1119:Dedicated short
1093:
1060:
1017:
1005:
999:
994:
951:
946:
933:
932:
925:
912:
908:
904:
871:
868:
867:
850:
847:
846:
797:
795:
792:
791:
756:
754:
751:
750:
704:
697:
693:
683:
679:
659:
616:
613:
612:
586:
583:
582:
556:
553:
552:
534:
509:
506:
505:
484:
476:
474:
466:
463:
462:
435:
427:
425:
420:
417:
416:
407:. 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:
1273:
1269:
1268:
1266:
1265:
1260:
1255:
1250:
1245:
1240:
1235:
1229:
1227:
1220:
1214:
1213:
1211:
1210:
1205:
1200:
1195:
1190:
1185:
1179:
1177:
1173:
1172:
1165:
1163:
1160:
1159:
1157:
1156:
1146:
1144:
1140:
1139:
1137:
1136:
1131:
1126:
1121:
1116:
1107:
1101:
1099:
1095:
1094:
1092:
1091:
1086:
1084:Risk arbitrage
1081:
1076:
1070:
1068:
1062:
1061:
1059:
1058:
1053:
1048:
1039:
1034:
1029:
1023:
1021:
1019:relative value
1007:
1001:
1000:
993:
992:
985:
978:
970:
964:
963:
958:
950:
949:External links
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233:Main article:
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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
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