1990:
486:
The future value of that asset's dividends (this could also be coupons from bonds, monthly rent from a house, fruit from a crop, etc.) is calculated using the risk-free force of interest. This is because we are in a risk-free situation (the whole point of the forward contract is to get rid of risk or
487:
to at least reduce it) so why would the owner of the asset take any chances? He would reinvest at the risk-free rate (i.e. U.S. T-bills which are considered risk-free). The spot price of the asset is simply the market value at the instant in time when the forward contract is entered into. So
189:
462:
The two questions here are what price the short position (the seller of the asset) should offer to maximize his gain, and what price the long position (the buyer of the asset) should accept to maximize his gain?
824:
469:
The short position knows as much as the long position knows: the short/long positions are both aware of any schemes that they could partake on to gain a profit given some forward price.
903:
452:
651:
697:
593:
410:
379:
346:
263:
908:
Notice that implicit in the above derivation is the assumption that the underlying can be traded. This assumption does not hold for certain kinds of forwards.
314:
289:
235:
215:
1533:
1108:
1873:
57:
1563:
1004:
1695:
713:
1431:
1933:
1101:
39:
assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the
928:
2015:
1868:
1513:
2020:
1908:
1446:
1300:
1094:
1527:
1705:
1809:
1620:
495:
of keeping the asset for that time period (he could have sold it and invested the money at the risk-free rate).
1928:
1923:
1578:
1523:
1878:
1548:
1538:
1406:
1247:
1179:
292:
1827:
1675:
1660:
1625:
1568:
1888:
1739:
1655:
1232:
939:. The forward measure and the risk neutral measure are the same when interest rates are deterministic.
1553:
853:
415:
1842:
1799:
1789:
1779:
1500:
1441:
1376:
1330:
1325:
1199:
1159:
1126:
936:
924:
604:
266:
1558:
1847:
1635:
1381:
659:
1898:
1883:
1852:
1837:
1804:
1670:
1461:
1426:
1189:
1154:
1117:
559:
1903:
1893:
1832:
1819:
1794:
1680:
1466:
1262:
1049:
1010:
1000:
958:
317:
43:
and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task.
1784:
1774:
1764:
1723:
1718:
1700:
1630:
1396:
1391:
1363:
1315:
1194:
1134:
1041:
492:
472:
So of course they will have to settle on a fair price or else the transaction cannot occur.
36:
32:
388:
357:
324:
241:
1994:
1964:
1959:
1913:
1749:
1744:
1690:
1600:
1508:
1481:
1421:
1416:
1386:
1335:
1320:
1237:
1217:
953:
932:
51:
If the underlying asset is tradable and a dividend exists, the forward price is given by:
479:(fair price + future value of asset's dividends) − spot price of asset = cost of capital
1969:
1954:
1754:
1665:
1615:
1592:
1573:
1401:
1343:
1310:
1305:
1285:
1209:
299:
274:
220:
200:
16:
Future cost agreed upon by a buyer and seller of something to be traded at a later time
2009:
1949:
1918:
1685:
1645:
1640:
1476:
1348:
1295:
1290:
1272:
1169:
1149:
968:
963:
1769:
1543:
1471:
1451:
1411:
1280:
1252:
1242:
1184:
948:
24:
1078:
1070:
916:
There is a difference between forward and futures prices when interest rates are
1650:
1518:
1489:
1485:
1436:
1227:
1222:
466:
At the very least we know that both do not want to lose any money in the deal.
1974:
1610:
1605:
1371:
1257:
1045:
917:
349:
40:
1053:
1014:
1164:
1989:
1029:
994:
184:{\displaystyle F=S_{0}e^{(r-q)T}-\sum _{i=1}^{N}D_{i}e^{(r-q)(T-t_{i})}\,}
1734:
1456:
1353:
1174:
973:
382:
1086:
920:. This difference disappears when interest rates are deterministic.
28:
819:{\displaystyle F=c_{1}e^{r(T-t_{1})}+\cdots +c_{n}e^{r(T-t_{n})}}
1090:
553:
Solving for fair price and substituting mathematics we get:
999:. Robert J. Elliott. New York, NY: Springer. p. 41.
549:= length of time from when the contract was entered into
269:(used for calculating continuous compounding interests)
935:, whereas the futures price is a martingale under the
856:
716:
703:
is the effective rate of interest per time period of
662:
607:
562:
418:
391:
360:
327:
302:
277:
244:
223:
203:
60:
352:
of the asset (i.e. what it would sell for at time 0)
1942:
1861:
1818:
1714:
1591:
1499:
1362:
1271:
1208:
1142:
1133:
897:
818:
691:
645:
587:
446:
404:
373:
340:
308:
283:
257:
229:
209:
183:
543:= risk-free interest rate compounded continuously
1102:
1034:Review of Quantitative Finance and Accounting
1030:"A Note on Forward Price and Forward Measure"
1028:Chen, Ren-Raw; Huang, Jing-Zhi (2002-11-01).
8:
1139:
1109:
1095:
1087:
482:forward price = spot price − cost of carry
894:
882:
855:
805:
788:
778:
754:
737:
727:
715:
688:
667:
661:
642:
624:
606:
584:
561:
429:
417:
396:
390:
365:
359:
332:
326:
301:
276:
249:
243:
222:
202:
180:
169:
140:
130:
120:
109:
81:
71:
59:
491:and his net gain can only come from the
217:is the forward price to be paid at time
1934:Power reverse dual-currency note (PRDC)
1874:Constant proportion portfolio insurance
1080:Martingale Methods in Financial Markets
985:
385:that is guaranteed to be paid at time
847:Doing some reduction we end up with:
7:
1869:Collateralized debt obligation (CDO)
475:An economic articulation would be:
523:= future value of asset's dividend
458:Proof of the forward price formula
14:
27:) is the agreed upon price of an
1988:
898:{\displaystyle K=(S-I)e^{rT}.\,}
447:{\displaystyle 0<t_{i}<T.}
646:{\displaystyle C=S(e^{rT}-1)\,}
1696:Year-on-year inflation-indexed
875:
863:
811:
792:
760:
741:
639:
617:
175:
156:
153:
141:
94:
82:
1:
1706:Zero-coupon inflation-indexed
912:Forward versus futures prices
1072:Binomial Models in Finance -
692:{\displaystyle e^{rT}=1+j\,}
1909:Foreign exchange derivative
1301:Callable bull/bear contract
993:Van der Hoek, John (2006).
2037:
1074:van der Hoek & Elliott
996:Binomial models in finance
1983:
1810:Stock market index future
1124:
1082:- Musiela & Rutkowski
927:, the forward price is a
588:{\displaystyle K=C+S-F\,}
1929:Mortgage-backed security
1924:Interest rate derivative
1899:Equity-linked note (ELN)
1884:Credit-linked note (CLN)
1879:Contract for difference
1180:Risk-free interest rate
1046:10.1023/A:1020715407939
293:risk-free interest rate
1661:Forward Rate Agreement
899:
840:dividend paid at time
820:
693:
647:
589:
448:
406:
375:
342:
310:
285:
259:
231:
211:
185:
125:
2016:Derivatives (finance)
1889:Credit default option
1233:Employee stock option
900:
821:
694:
648:
590:
517:= spot price of asset
449:
407:
405:{\displaystyle t_{i}}
376:
374:{\displaystyle D_{i}}
343:
341:{\displaystyle S_{0}}
311:
286:
260:
258:{\displaystyle e^{x}}
232:
212:
186:
105:
47:Forward price formula
1843:Inflation derivative
1828:Commodity derivative
1800:Single-stock futures
1790:Normal backwardation
1780:Interest rate future
1621:Conditional variance
1127:Derivative (finance)
937:risk-neutral measure
925:stochastic processes
854:
714:
660:
605:
560:
416:
389:
358:
325:
300:
275:
267:exponential function
242:
221:
201:
58:
2021:Financial economics
1995:Business portal
1848:Property derivative
923:In the language of
529:= present value of
489:OUT − IN = NET GAIN
1853:Weather derivative
1838:Freight derivative
1820:Exotic derivatives
1740:Commodities future
1427:Intermarket spread
1190:Synthetic position
1118:Derivatives market
895:
816:
689:
643:
585:
533:(discounted using
444:
402:
371:
338:
306:
281:
255:
227:
207:
181:
2003:
2002:
1904:Equity derivative
1894:Credit derivative
1862:Other derivatives
1833:Energy derivative
1795:Perpetual futures
1676:Overnight indexed
1626:Constant maturity
1587:
1586:
1534:Finite difference
1467:Protective option
1006:978-0-387-31607-9
959:Convenience yield
511:= cost of capital
318:convenience yield
309:{\displaystyle q}
284:{\displaystyle r}
230:{\displaystyle T}
210:{\displaystyle F}
2028:
1993:
1992:
1765:Forwards pricing
1539:Garman–Kohlhagen
1140:
1111:
1104:
1097:
1088:
1058:
1057:
1025:
1019:
1018:
990:
904:
902:
901:
896:
890:
889:
825:
823:
822:
817:
815:
814:
810:
809:
783:
782:
764:
763:
759:
758:
732:
731:
698:
696:
695:
690:
675:
674:
652:
650:
649:
644:
632:
631:
594:
592:
591:
586:
493:opportunity cost
490:
453:
451:
450:
445:
434:
433:
411:
409:
408:
403:
401:
400:
380:
378:
377:
372:
370:
369:
347:
345:
344:
339:
337:
336:
315:
313:
312:
307:
290:
288:
287:
282:
264:
262:
261:
256:
254:
253:
236:
234:
233:
228:
216:
214:
213:
208:
190:
188:
187:
182:
179:
178:
174:
173:
135:
134:
124:
119:
101:
100:
76:
75:
37:rational pricing
33:forward contract
2036:
2035:
2031:
2030:
2029:
2027:
2026:
2025:
2006:
2005:
2004:
1999:
1987:
1979:
1965:Great Recession
1960:Government debt
1938:
1914:Fund derivative
1857:
1814:
1775:Futures pricing
1750:Dividend future
1745:Currency future
1728:
1710:
1583:
1559:Put–call parity
1495:
1482:Vertical spread
1417:Diagonal spread
1387:Calendar spread
1358:
1267:
1204:
1129:
1120:
1115:
1067:
1062:
1061:
1027:
1026:
1022:
1007:
992:
991:
987:
982:
954:Forward measure
945:
933:forward measure
914:
878:
852:
851:
834:
801:
784:
774:
750:
733:
723:
712:
711:
663:
658:
657:
620:
603:
602:
558:
557:
488:
460:
425:
414:
413:
392:
387:
386:
361:
356:
355:
328:
323:
322:
298:
297:
273:
272:
245:
240:
239:
219:
218:
199:
198:
165:
136:
126:
77:
67:
56:
55:
49:
17:
12:
11:
5:
2034:
2032:
2024:
2023:
2018:
2008:
2007:
2001:
2000:
1998:
1997:
1984:
1981:
1980:
1978:
1977:
1972:
1970:Municipal debt
1967:
1962:
1957:
1955:Corporate debt
1952:
1946:
1944:
1940:
1939:
1937:
1936:
1931:
1926:
1921:
1916:
1911:
1906:
1901:
1896:
1891:
1886:
1881:
1876:
1871:
1865:
1863:
1859:
1858:
1856:
1855:
1850:
1845:
1840:
1835:
1830:
1824:
1822:
1816:
1815:
1813:
1812:
1807:
1802:
1797:
1792:
1787:
1782:
1777:
1772:
1767:
1762:
1757:
1755:Forward market
1752:
1747:
1742:
1737:
1731:
1729:
1727:
1726:
1721:
1715:
1712:
1711:
1709:
1708:
1703:
1698:
1693:
1688:
1683:
1678:
1673:
1668:
1663:
1658:
1653:
1648:
1643:
1638:
1636:Credit default
1633:
1628:
1623:
1618:
1613:
1608:
1603:
1597:
1595:
1589:
1588:
1585:
1584:
1582:
1581:
1576:
1571:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1521:
1516:
1511:
1505:
1503:
1497:
1496:
1494:
1493:
1479:
1474:
1469:
1464:
1459:
1454:
1449:
1444:
1439:
1434:
1432:Iron butterfly
1429:
1424:
1419:
1414:
1409:
1404:
1402:Covered option
1399:
1394:
1389:
1384:
1379:
1374:
1368:
1366:
1360:
1359:
1357:
1356:
1351:
1346:
1341:
1340:Mountain range
1338:
1333:
1328:
1323:
1318:
1313:
1308:
1303:
1298:
1293:
1288:
1283:
1277:
1275:
1269:
1268:
1266:
1265:
1260:
1255:
1250:
1245:
1240:
1235:
1230:
1225:
1220:
1214:
1212:
1206:
1205:
1203:
1202:
1197:
1192:
1187:
1182:
1177:
1172:
1167:
1162:
1157:
1152:
1146:
1144:
1137:
1131:
1130:
1125:
1122:
1121:
1116:
1114:
1113:
1106:
1099:
1091:
1085:
1084:
1076:
1066:
1063:
1060:
1059:
1040:(3): 261–272.
1020:
1005:
984:
983:
981:
978:
977:
976:
971:
966:
961:
956:
951:
944:
941:
913:
910:
906:
905:
893:
888:
885:
881:
877:
874:
871:
868:
865:
862:
859:
832:
827:
826:
813:
808:
804:
800:
797:
794:
791:
787:
781:
777:
773:
770:
767:
762:
757:
753:
749:
746:
743:
740:
736:
730:
726:
722:
719:
687:
684:
681:
678:
673:
670:
666:
654:
653:
641:
638:
635:
630:
627:
623:
619:
616:
613:
610:
596:
595:
583:
580:
577:
574:
571:
568:
565:
551:
550:
544:
538:
524:
518:
512:
506:
484:
483:
480:
459:
456:
455:
454:
443:
440:
437:
432:
428:
424:
421:
399:
395:
368:
364:
353:
335:
331:
320:
305:
295:
280:
270:
252:
248:
237:
226:
206:
192:
191:
177:
172:
168:
164:
161:
158:
155:
152:
149:
146:
143:
139:
133:
129:
123:
118:
115:
112:
108:
104:
99:
96:
93:
90:
87:
84:
80:
74:
70:
66:
63:
48:
45:
23:(or sometimes
15:
13:
10:
9:
6:
4:
3:
2:
2033:
2022:
2019:
2017:
2014:
2013:
2011:
1996:
1991:
1986:
1985:
1982:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1951:
1950:Consumer debt
1948:
1947:
1945:
1943:Market issues
1941:
1935:
1932:
1930:
1927:
1925:
1922:
1920:
1919:Fund of funds
1917:
1915:
1912:
1910:
1907:
1905:
1902:
1900:
1897:
1895:
1892:
1890:
1887:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1866:
1864:
1860:
1854:
1851:
1849:
1846:
1844:
1841:
1839:
1836:
1834:
1831:
1829:
1826:
1825:
1823:
1821:
1817:
1811:
1808:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1786:
1783:
1781:
1778:
1776:
1773:
1771:
1768:
1766:
1763:
1761:
1760:Forward price
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1732:
1730:
1725:
1722:
1720:
1717:
1716:
1713:
1707:
1704:
1702:
1699:
1697:
1694:
1692:
1689:
1687:
1684:
1682:
1679:
1677:
1674:
1672:
1671:Interest rate
1669:
1667:
1664:
1662:
1659:
1657:
1654:
1652:
1649:
1647:
1644:
1642:
1639:
1637:
1634:
1632:
1629:
1627:
1624:
1622:
1619:
1617:
1614:
1612:
1609:
1607:
1604:
1602:
1599:
1598:
1596:
1594:
1590:
1580:
1577:
1575:
1572:
1570:
1567:
1565:
1564:MC Simulation
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1529:
1525:
1524:Black–Scholes
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1506:
1504:
1502:
1498:
1491:
1487:
1483:
1480:
1478:
1477:Risk reversal
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1458:
1455:
1453:
1450:
1448:
1445:
1443:
1440:
1438:
1435:
1433:
1430:
1428:
1425:
1423:
1420:
1418:
1415:
1413:
1410:
1408:
1407:Credit spread
1405:
1403:
1400:
1398:
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1378:
1375:
1373:
1370:
1369:
1367:
1365:
1361:
1355:
1352:
1350:
1347:
1345:
1342:
1339:
1337:
1334:
1332:
1331:Interest rate
1329:
1327:
1326:Forward start
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1278:
1276:
1274:
1270:
1264:
1261:
1259:
1256:
1254:
1253:Option styles
1251:
1249:
1246:
1244:
1241:
1239:
1236:
1234:
1231:
1229:
1226:
1224:
1221:
1219:
1216:
1215:
1213:
1211:
1207:
1201:
1198:
1196:
1193:
1191:
1188:
1186:
1183:
1181:
1178:
1176:
1173:
1171:
1170:Open interest
1168:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1150:Delta neutral
1148:
1147:
1145:
1141:
1138:
1136:
1132:
1128:
1123:
1119:
1112:
1107:
1105:
1100:
1098:
1093:
1092:
1089:
1083:
1081:
1077:
1075:
1073:
1069:
1068:
1064:
1055:
1051:
1047:
1043:
1039:
1035:
1031:
1024:
1021:
1016:
1012:
1008:
1002:
998:
997:
989:
986:
979:
975:
972:
970:
969:Backwardation
967:
965:
964:Cost of carry
962:
960:
957:
955:
952:
950:
947:
946:
942:
940:
938:
934:
930:
926:
921:
919:
911:
909:
891:
886:
883:
879:
872:
869:
866:
860:
857:
850:
849:
848:
845:
843:
839:
835:
806:
802:
798:
795:
789:
785:
779:
775:
771:
768:
765:
755:
751:
747:
744:
738:
734:
728:
724:
720:
717:
710:
709:
708:
706:
702:
685:
682:
679:
676:
671:
668:
664:
636:
633:
628:
625:
621:
614:
611:
608:
601:
600:
599:
581:
578:
575:
572:
569:
566:
563:
556:
555:
554:
548:
545:
542:
539:
536:
532:
528:
525:
522:
519:
516:
513:
510:
507:
504:
501:
500:
499:
496:
494:
481:
478:
477:
476:
473:
470:
467:
464:
457:
441:
438:
435:
430:
426:
422:
419:
397:
393:
384:
366:
362:
354:
351:
333:
329:
321:
319:
303:
296:
294:
278:
271:
268:
250:
246:
238:
224:
204:
197:
196:
195:
170:
166:
162:
159:
150:
147:
144:
137:
131:
127:
121:
116:
113:
110:
106:
102:
97:
91:
88:
85:
78:
72:
68:
64:
61:
54:
53:
52:
46:
44:
42:
38:
34:
30:
26:
22:
21:forward price
1770:Forward rate
1759:
1681:Total return
1569:Real options
1472:Ratio spread
1452:Naked option
1412:Debit spread
1243:Fixed income
1185:Strike price
1079:
1071:
1065:Bibliography
1037:
1033:
1023:
995:
988:
949:Forward rate
922:
915:
907:
846:
841:
837:
830:
828:
704:
700:
655:
597:
552:
546:
540:
534:
530:
526:
520:
514:
508:
505:= fair price
502:
497:
485:
474:
471:
468:
465:
461:
193:
50:
35:. Using the
25:forward rate
20:
18:
1701:Zero Coupon
1631:Correlation
1579:Vanna–Volga
1437:Iron condor
1223:Bond option
2010:Categories
1975:Tax policy
1691:Volatility
1601:Amortising
1442:Jelly roll
1377:Box spread
1372:Backspread
1364:Strategies
1200:Volatility
1195:the Greeks
1160:Expiration
980:References
931:under the
929:martingale
918:stochastic
350:spot price
41:spot price
1666:Inflation
1616:Commodity
1574:Trinomial
1509:Bachelier
1501:Valuation
1382:Butterfly
1316:Commodore
1165:Moneyness
1054:1573-7179
1015:209909002
870:−
799:−
769:⋯
748:−
634:−
579:−
163:−
148:−
107:∑
103:−
89:−
1805:Slippage
1735:Contango
1719:Forwards
1686:Variance
1646:Dividend
1641:Currency
1554:Margrabe
1549:Lattices
1528:equation
1514:Binomial
1462:Strangle
1457:Straddle
1354:Swaption
1336:Lookback
1321:Compound
1263:Warrants
1238:European
1218:American
1210:Vanillas
1175:Pin risk
1155:Exercise
974:Contango
943:See also
383:dividend
1724:Futures
1344:Rainbow
1311:Cliquet
1306:Chooser
1286:Barrier
1273:Exotics
1135:Options
836:is the
656:(since
598:where:
348:is the
316:is the
291:is the
265:is the
1785:Margin
1651:Equity
1544:Heston
1447:Ladder
1397:Condor
1392:Collar
1349:Spread
1296:Binary
1291:Basket
1052:
1013:
1003:
829:where
699:where
412:where
194:where
1656:Forex
1611:Basis
1606:Asset
1593:Swaps
1519:Black
1422:Fence
1281:Asian
1143:Terms
381:is a
31:in a
29:asset
1490:Bull
1486:Bear
1228:Call
1050:ISSN
1011:OCLC
1001:ISBN
498:let
436:<
423:<
19:The
1258:Put
1042:doi
2012::
1488:,
1248:FX
1048:.
1038:19
1036:.
1032:.
1009:.
844:.
842:t
707:)
1530:)
1526:(
1492:)
1484:(
1110:e
1103:t
1096:v
1056:.
1044::
1017:.
892:.
887:T
884:r
880:e
876:)
873:I
867:S
864:(
861:=
858:K
838:i
833:i
831:c
812:)
807:n
803:t
796:T
793:(
790:r
786:e
780:n
776:c
772:+
766:+
761:)
756:1
752:t
745:T
742:(
739:r
735:e
729:1
725:c
721:=
718:F
705:T
701:j
686:j
683:+
680:1
677:=
672:T
669:r
665:e
640:)
637:1
629:T
626:r
622:e
618:(
615:S
612:=
609:C
582:F
576:S
573:+
570:C
567:=
564:K
547:T
541:r
537:)
535:r
531:F
527:I
521:F
515:S
509:C
503:K
442:.
439:T
431:i
427:t
420:0
398:i
394:t
367:i
363:D
334:0
330:S
304:q
279:r
251:x
247:e
225:T
205:F
176:)
171:i
167:t
160:T
157:(
154:)
151:q
145:r
142:(
138:e
132:i
128:D
122:N
117:1
114:=
111:i
98:T
95:)
92:q
86:r
83:(
79:e
73:0
69:S
65:=
62:F
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