2499:
768:
is the foreign currency risk-free interest rate (where domestic currency is the currency in which we obtain the value of the option; the formula also requires that FX rates – both strike and current spot be quoted in terms of "units of domestic currency per unit of foreign currency"). The results are
709:
The earliest currency options pricing model was published by Biger and Hull, (Financial
Management, spring 1983). The model preceded the Garman and Kolhagen's Model. In 1983 Garman and Kohlhagen extended the Black–Scholes model to cope with the presence of two interest rates (one for each currency).
373:
If the rate is lower than 2.0000 on
December 31 (say 1.9000), meaning that the dollar is stronger and the pound is weaker, then the option is exercised, allowing the owner to sell GBP at 2.0000 and immediately buy it back in the spot market at 1.9000, making a profit of (2.0000 GBPUSD −
503:
The difference between FX options and traditional options is that in the latter case the trade is to give an amount of money and receive the right to buy or sell a commodity, stock or other non-money asset. In FX options, the asset in question is also money, denominated in another currency.
1189:
1048:
904:
1456:
An earlier pricing model was published by Biger and Hull, Financial
Management, spring 1983. The model preceded Garman and Kolhagen Model. A wide range of techniques are in use for calculating the options risk exposure, or
374:
1.9000 GBPUSD) × 1,000,000 GBP = 100,000 USD in the process. If instead they take the profit in GBP (by selling the USD on the spot market) this amounts to 100,000 / 1.9000 = 52,632 GBP.
1465:). Although the option prices produced by every model agree (with Garman–Kohlhagen), risk numbers can vary significantly depending on the assumptions used for the properties of spot price movements,
494:
In the money – for a put option, this is when the current price is less than the strike price, and would thus generate a profit were it exercised; for a call option the situation is inverted.
1243:
507:
For example, a call option on oil allows the investor to buy oil at a given price and date. The investor on the other side of the trade is in effect selling a put option on the currency.
549:
profit), but has a non-linear GBP value. Conversely, the GBP value is linear in the USDGBP rate, while the USD value is non-linear. This is because inverting a rate has the effect of
1330:
663:
Using options, the UK firm can purchase a GBP call/USD put option (the right to sell part or all of their expected income for pounds sterling at a predetermined rate), which:
581:
489:
1441:
1392:
1359:
1273:
766:
735:
1060:
916:
1414:
1295:
778:
2042:
1617:
255:
637:, then the UK firm receives more GBP. This uncertainty exposes the firm to FX risk. Assuming that the cash flow is certain, the firm can enter into a
1505:
2382:
649:. This forward contract is free, and, presuming the expected cash arrives, exactly matches the firm's exposure, perfectly hedging their FX risk.
335:
For example, a GBPUSD contract could give the owner the right to sell £1,000,000 and buy $ 2,000,000 on
December 31. In this case the pre-agreed
2072:
343:, is 2.0000 USD per GBP (or GBP/USD 2.00 as it is typically quoted) and the notional amounts (notionals) are £1,000,000 and $ 2,000,000.
2204:
443:
Non-linear payoff – the payoff for a straightforward FX option is linear in the underlying currency, denominating the payout in a given
324:
1940:
308:
2524:
2442:
1610:
116:
2534:
2377:
2022:
395:
Foreign exchange option – the right to sell money in one currency and buy money in another currency at a fixed date and rate.
248:
518:
currency notionals, not the local currency notionals, else the foreign currencies received and delivered do not offset.
2417:
1955:
1809:
1603:
316:
312:
293:
2036:
1574:
1195:
2529:
2214:
304:
70:
2318:
2129:
241:
60:
2437:
2432:
178:
2087:
2032:
1462:
683:
1488:(e.g. for exchanging delta, or calculating the strike on a 25 delta option) Garman–Kohlhagen is always used.
2387:
2057:
1915:
1688:
738:
147:
106:
525:, as in the above example, an option on GBPUSD gives a USD value that is linear in GBPUSD using USD as the
2336:
2184:
2169:
2134:
2077:
450:
224:
75:
2397:
2248:
2164:
1741:
1477:
646:
229:
183:
152:
65:
2062:
1302:
284:
financial instrument that gives the right but not the obligation to exchange money denominated in one
2351:
2308:
2298:
2288:
2009:
1950:
1885:
1839:
1834:
1708:
1668:
1635:
1549:
1444:
1417:
695:
281:
85:
80:
55:
2067:
625:
for a piece of engineering equipment to be delivered in 90 days. If the GBP strengthens against the
2356:
2144:
1890:
552:
460:
2407:
2392:
2361:
2346:
2313:
2179:
1970:
1935:
1698:
1663:
1626:
457:
of an FX option depends on the numéraire of the purchaser, again because of the non-linearity of
454:
90:
629:
over the next 90 days the UK firm loses money, as it will receive less GBP after converting the
2412:
2402:
2341:
2328:
2303:
2189:
1975:
1771:
667:
protects the GBP value that the firm expects in 90 days' time (presuming the cash is received)
1426:
1184:{\displaystyle d_{1}={\frac {\ln(S_{0}/K)+(r_{d}-r_{f}+\sigma ^{2}/2)T}{\sigma {\sqrt {T}}}}}
769:
also in the same units and to be meaningful need to be converted into one of the currencies.
2293:
2283:
2273:
2232:
2227:
2209:
2139:
1905:
1900:
1872:
1824:
1703:
1643:
1481:
1466:
1458:
638:
320:
300:
209:
142:
111:
1370:
1337:
1251:
1043:{\displaystyle p=Ke^{-r_{d}T}{\mathcal {N}}(-d_{2})-S_{0}e^{-r_{f}T}{\mathcal {N}}(-d_{1})}
744:
713:
2503:
2473:
2468:
2422:
2258:
2253:
2199:
2109:
2017:
1990:
1930:
1925:
1895:
1844:
1829:
1746:
1726:
1362:
699:
592:
416:
137:
899:{\displaystyle c=S_{0}e^{-r_{f}T}{\mathcal {N}}(d_{1})-Ke^{-r_{d}T}{\mathcal {N}}(d_{2})}
652:
If the cash flow is uncertain, a forward FX contract exposes the firm to FX risk in the
2478:
2463:
2263:
2174:
2124:
2101:
2082:
1910:
1852:
1819:
1814:
1794:
1718:
1399:
1280:
618:
355:
17:
323:. The global market for exchange-traded currency options was notionally valued by the
2518:
2458:
2427:
2268:
2194:
2154:
2149:
1985:
1857:
1804:
1799:
1781:
1678:
1658:
687:
511:
410:
336:
289:
219:
214:
193:
157:
50:
45:
670:
costs at most the option premium (unlike a forward, which can have unlimited losses)
2278:
2052:
1980:
1960:
1920:
1789:
1761:
1751:
1693:
1485:
673:
yields a profit if the expected cash is not received but FX rates move in its favor
398:
340:
188:
526:
444:
437:
419:– the amount of each currency that the option allows the investor to sell or buy.
2159:
2027:
1998:
1994:
1945:
1736:
1731:
1470:
691:
383:
347:
772:
Then the domestic currency value of a call option into the foreign currency is
2483:
2119:
2114:
1880:
1766:
703:
404:
389:
351:
1673:
2498:
702:
on an FX rate is typically calculated by assuming that the rate follows a
2243:
1965:
1862:
1683:
307:
and is lightly regulated, but a fraction is traded on exchanges like the
285:
132:
598:
future cash flows in a foreign currency. The general rule is to hedge
1595:
299:
The foreign exchange options market is the deepest, largest and most
1523:
1506:
Foreign
Exchange (FX) Terminologies: Forward Deal and Options Deal
1416:
is the time to maturity (calculated according to the appropriate
1599:
401:– the asset price at which the investor can exercise an option.
1509:
1308:
1016:
954:
875:
823:
2047:
1550:"British Pound (GBP) to Euro (EUR) exchange rate history"
413:– the price of the asset for delivery at a future time.
392:– the right to sell an asset at a fixed date and price.
660:
received, typically making an option a better choice.
386:– the right to buy an asset at a fixed date and price.
1429:
1402:
1373:
1340:
1305:
1283:
1254:
1198:
1063:
919:
781:
747:
716:
656:
direction, in the case that the expected USD cash is
555:
463:
645:
in 90 days time, in exchange for GBP at the current
2451:
2370:
2327:
2223:
2100:
2008:
1871:
1780:
1717:
1651:
1642:
1476:After Garman–Kohlhagen, the most common models are
1435:
1408:
1386:
1353:
1324:
1289:
1267:
1237:
1183:
1042:
898:
760:
729:
633:into GBP. However, if the GBP weakens against the
575:
483:
407:– the price of the asset at the time of the trade.
1332:is the cumulative normal distribution function
1238:{\displaystyle d_{2}=d_{1}-\sigma {\sqrt {T}}}
1611:
1484:, although when agreeing risk numbers with a
249:
8:
440:– the currency in which an asset is valued.
1648:
1618:
1604:
1596:
256:
242:
29:
1428:
1401:
1394:is foreign risk free simple interest rate
1378:
1372:
1345:
1339:
1307:
1306:
1304:
1282:
1259:
1253:
1228:
1216:
1203:
1197:
1171:
1152:
1146:
1133:
1120:
1099:
1093:
1077:
1068:
1062:
1031:
1015:
1014:
1003:
995:
985:
969:
953:
952:
941:
933:
918:
887:
874:
873:
862:
854:
835:
822:
821:
810:
802:
792:
780:
752:
746:
721:
715:
591:Corporations primarily use FX options to
565:
554:
473:
462:
303:for options of any kind. Most trading is
366:; although it could equally be called a
2443:Power reverse dual-currency note (PRDC)
2383:Constant proportion portfolio insurance
1497:
741:to expiry of the domestic currency and
529:(a move from 2.0000 to 1.9000 yields a
201:
170:
124:
98:
37:
32:
678:Valuation: the Garman–Kohlhagen model
621:manufacturing firm expects to be paid
288:into another currency at a pre-agreed
7:
2378:Collateralized debt obligation (CDO)
1575:"Currency options pricing explained"
909:The value of a put option has value
1528:Link International Exchange Company
1524:"Fastest Currency Exchange Company"
325:Bank for International Settlements
25:
1325:{\displaystyle {\mathcal {N}}(x)}
602:foreign currency cash flows with
521:In the case of an FX option on a
309:International Securities Exchange
2497:
346:This type of contract is both a
1510:International Business Times AU
117:Retail foreign exchange trading
27:Derivative financial instrument
2205:Year-on-year inflation-indexed
1319:
1313:
1160:
1113:
1107:
1086:
1037:
1021:
975:
959:
893:
880:
841:
828:
559:
467:
1:
2215:Zero-coupon inflation-indexed
327:at $ 158.3 trillion in 2005.
576:{\displaystyle x\mapsto 1/x}
484:{\displaystyle x\mapsto 1/x}
358:, and is typically called a
272:(commonly shortened to just
2418:Foreign exchange derivative
1810:Callable bull/bear contract
317:Chicago Mercantile Exchange
313:Philadelphia Stock Exchange
294:Foreign exchange derivative
2551:
2492:
2319:Stock market index future
1633:
1579:www.derivativepricing.com
422:Ratio of notionals – the
292:on a specified date. See
61:Exchange-rate flexibility
2438:Mortgage-backed security
2433:Interest rate derivative
2408:Equity-linked note (ELN)
2393:Credit-linked note (CLN)
1554:www.exchangerates.org.uk
1275:is the current spot rate
610:foreign cash flows with
362:, as it is a put on the
179:Bretton Woods Conference
2525:Foreign exchange market
2388:Contract for difference
1689:Risk-free interest rate
1436:{\displaystyle \sigma }
739:risk-free interest rate
583:, which is non-linear.
270:foreign exchange option
163:Foreign exchange option
148:Non-deliverable forward
107:Foreign exchange market
18:Foreign-exchange option
2170:Forward Rate Agreement
1437:
1410:
1388:
1361:is domestic risk free
1355:
1326:
1291:
1269:
1239:
1185:
1044:
900:
762:
731:
577:
485:
305:over the counter (OTC)
225:Foreign exchange fraud
76:Floating exchange rate
2535:Derivatives (finance)
2398:Credit default option
1742:Employee stock option
1512:on February 14, 2011.
1438:
1411:
1389:
1387:{\displaystyle r_{f}}
1356:
1354:{\displaystyle r_{d}}
1327:
1292:
1270:
1268:{\displaystyle S_{0}}
1240:
1186:
1045:
901:
763:
761:{\displaystyle r_{f}}
732:
730:{\displaystyle r_{d}}
696:interest rate options
647:forward exchange rate
578:
486:
230:Currency intervention
184:Smithsonian Agreement
171:Historical agreements
153:Foreign exchange swap
2352:Inflation derivative
2337:Commodity derivative
2309:Single-stock futures
2299:Normal backwardation
2289:Interest rate future
2130:Conditional variance
1636:Derivative (finance)
1471:interest rate curves
1461:(as for example the
1427:
1418:day count convention
1400:
1371:
1338:
1303:
1281:
1252:
1196:
1061:
917:
779:
745:
714:
553:
514:, traders match the
461:
86:Managed float regime
81:Linked exchange rate
56:Exchange rate regime
2504:Business portal
2357:Property derivative
1508:" Published by the
1297:is the strike price
684:Black–Scholes model
451:Change of numéraire
71:Fixed exchange rate
2362:Weather derivative
2347:Freight derivative
2329:Exotic derivatives
2249:Commodities future
1936:Intermarket spread
1699:Synthetic position
1627:Derivatives market
1522:Hammad, Muhammad.
1467:volatility surface
1463:Vanna-Volga method
1433:
1406:
1384:
1351:
1322:
1287:
1265:
1235:
1181:
1040:
896:
758:
727:
573:
481:
455:implied volatility
426:, not the current
91:Dual exchange rate
2530:Options (finance)
2512:
2511:
2413:Equity derivative
2403:Credit derivative
2371:Other derivatives
2342:Energy derivative
2304:Perpetual futures
2185:Overnight indexed
2135:Constant maturity
2096:
2095:
2043:Finite difference
1976:Protective option
1409:{\displaystyle T}
1290:{\displaystyle K}
1233:
1179:
1176:
698:, the value of a
350:on dollars and a
321:futures contracts
266:
265:
16:(Redirected from
2542:
2502:
2501:
2274:Forwards pricing
2048:Garman–Kohlhagen
1649:
1620:
1613:
1606:
1597:
1590:
1589:
1587:
1585:
1571:
1565:
1564:
1562:
1560:
1546:
1540:
1539:
1537:
1535:
1519:
1513:
1502:
1482:local volatility
1442:
1440:
1439:
1434:
1415:
1413:
1412:
1407:
1393:
1391:
1390:
1385:
1383:
1382:
1360:
1358:
1357:
1352:
1350:
1349:
1331:
1329:
1328:
1323:
1312:
1311:
1296:
1294:
1293:
1288:
1274:
1272:
1271:
1266:
1264:
1263:
1244:
1242:
1241:
1236:
1234:
1229:
1221:
1220:
1208:
1207:
1190:
1188:
1187:
1182:
1180:
1178:
1177:
1172:
1166:
1156:
1151:
1150:
1138:
1137:
1125:
1124:
1103:
1098:
1097:
1078:
1073:
1072:
1049:
1047:
1046:
1041:
1036:
1035:
1020:
1019:
1013:
1012:
1008:
1007:
990:
989:
974:
973:
958:
957:
951:
950:
946:
945:
905:
903:
902:
897:
892:
891:
879:
878:
872:
871:
867:
866:
840:
839:
827:
826:
820:
819:
815:
814:
797:
796:
767:
765:
764:
759:
757:
756:
736:
734:
733:
728:
726:
725:
644:
639:forward contract
636:
632:
628:
624:
582:
580:
579:
574:
569:
548:
546:
544:
543:
540:
537:
490:
488:
487:
482:
477:
258:
251:
244:
210:Bureau de change
143:Currency forward
112:Futures exchange
33:Foreign exchange
30:
21:
2550:
2549:
2545:
2544:
2543:
2541:
2540:
2539:
2515:
2514:
2513:
2508:
2496:
2488:
2474:Great Recession
2469:Government debt
2447:
2423:Fund derivative
2366:
2323:
2284:Futures pricing
2259:Dividend future
2254:Currency future
2237:
2219:
2092:
2068:Put–call parity
2004:
1991:Vertical spread
1926:Diagonal spread
1896:Calendar spread
1867:
1776:
1713:
1638:
1629:
1624:
1594:
1593:
1583:
1581:
1573:
1572:
1568:
1558:
1556:
1548:
1547:
1543:
1533:
1531:
1521:
1520:
1516:
1503:
1499:
1494:
1454:
1452:Risk management
1447:of the FX rate.
1425:
1424:
1398:
1397:
1374:
1369:
1368:
1363:simple interest
1341:
1336:
1335:
1301:
1300:
1279:
1278:
1255:
1250:
1249:
1212:
1199:
1194:
1193:
1167:
1142:
1129:
1116:
1089:
1079:
1064:
1059:
1058:
1050:
1027:
999:
991:
981:
965:
937:
929:
915:
914:
883:
858:
850:
831:
806:
798:
788:
777:
776:
748:
743:
742:
717:
712:
711:
700:European option
680:
642:
641:to deliver the
634:
630:
626:
622:
589:
551:
550:
541:
538:
535:
534:
532:
530:
501:
459:
458:
380:
333:
319:for options on
278:currency option
262:
138:Currency future
28:
23:
22:
15:
12:
11:
5:
2548:
2546:
2538:
2537:
2532:
2527:
2517:
2516:
2510:
2509:
2507:
2506:
2493:
2490:
2489:
2487:
2486:
2481:
2479:Municipal debt
2476:
2471:
2466:
2464:Corporate debt
2461:
2455:
2453:
2449:
2448:
2446:
2445:
2440:
2435:
2430:
2425:
2420:
2415:
2410:
2405:
2400:
2395:
2390:
2385:
2380:
2374:
2372:
2368:
2367:
2365:
2364:
2359:
2354:
2349:
2344:
2339:
2333:
2331:
2325:
2324:
2322:
2321:
2316:
2311:
2306:
2301:
2296:
2291:
2286:
2281:
2276:
2271:
2266:
2264:Forward market
2261:
2256:
2251:
2246:
2240:
2238:
2236:
2235:
2230:
2224:
2221:
2220:
2218:
2217:
2212:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2172:
2167:
2162:
2157:
2152:
2147:
2145:Credit default
2142:
2137:
2132:
2127:
2122:
2117:
2112:
2106:
2104:
2098:
2097:
2094:
2093:
2091:
2090:
2085:
2080:
2075:
2070:
2065:
2060:
2055:
2050:
2045:
2040:
2030:
2025:
2020:
2014:
2012:
2006:
2005:
2003:
2002:
1988:
1983:
1978:
1973:
1968:
1963:
1958:
1953:
1948:
1943:
1941:Iron butterfly
1938:
1933:
1928:
1923:
1918:
1913:
1911:Covered option
1908:
1903:
1898:
1893:
1888:
1883:
1877:
1875:
1869:
1868:
1866:
1865:
1860:
1855:
1850:
1849:Mountain range
1847:
1842:
1837:
1832:
1827:
1822:
1817:
1812:
1807:
1802:
1797:
1792:
1786:
1784:
1778:
1777:
1775:
1774:
1769:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1723:
1721:
1715:
1714:
1712:
1711:
1706:
1701:
1696:
1691:
1686:
1681:
1676:
1671:
1666:
1661:
1655:
1653:
1646:
1640:
1639:
1634:
1631:
1630:
1625:
1623:
1622:
1615:
1608:
1600:
1592:
1591:
1566:
1541:
1514:
1496:
1495:
1493:
1490:
1453:
1450:
1449:
1448:
1432:
1421:
1405:
1395:
1381:
1377:
1366:
1348:
1344:
1333:
1321:
1318:
1315:
1310:
1298:
1286:
1276:
1262:
1258:
1246:
1245:
1232:
1227:
1224:
1219:
1215:
1211:
1206:
1202:
1191:
1175:
1170:
1165:
1162:
1159:
1155:
1149:
1145:
1141:
1136:
1132:
1128:
1123:
1119:
1115:
1112:
1109:
1106:
1102:
1096:
1092:
1088:
1085:
1082:
1076:
1071:
1067:
1052:
1051:
1039:
1034:
1030:
1026:
1023:
1018:
1011:
1006:
1002:
998:
994:
988:
984:
980:
977:
972:
968:
964:
961:
956:
949:
944:
940:
936:
932:
928:
925:
922:
913:
907:
906:
895:
890:
886:
882:
877:
870:
865:
861:
857:
853:
849:
846:
843:
838:
834:
830:
825:
818:
813:
809:
805:
801:
795:
791:
787:
784:
755:
751:
724:
720:
679:
676:
675:
674:
671:
668:
619:United Kingdom
588:
585:
572:
568:
564:
561:
558:
500:
497:
496:
495:
492:
480:
476:
472:
469:
466:
448:
441:
435:
420:
414:
408:
402:
396:
393:
387:
379:
376:
332:
329:
268:In finance, a
264:
263:
261:
260:
253:
246:
238:
235:
234:
233:
232:
227:
222:
217:
212:
204:
203:
199:
198:
197:
196:
191:
186:
181:
173:
172:
168:
167:
166:
165:
160:
155:
150:
145:
140:
135:
127:
126:
122:
121:
120:
119:
114:
109:
101:
100:
96:
95:
94:
93:
88:
83:
78:
73:
68:
63:
58:
53:
48:
40:
39:
38:Exchange rates
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2547:
2536:
2533:
2531:
2528:
2526:
2523:
2522:
2520:
2505:
2500:
2495:
2494:
2491:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2460:
2459:Consumer debt
2457:
2456:
2454:
2452:Market issues
2450:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2428:Fund of funds
2426:
2424:
2421:
2419:
2416:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2384:
2381:
2379:
2376:
2375:
2373:
2369:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2334:
2332:
2330:
2326:
2320:
2317:
2315:
2312:
2310:
2307:
2305:
2302:
2300:
2297:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2272:
2270:
2269:Forward price
2267:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2245:
2242:
2241:
2239:
2234:
2231:
2229:
2226:
2225:
2222:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2180:Interest rate
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2107:
2105:
2103:
2099:
2089:
2086:
2084:
2081:
2079:
2076:
2074:
2073:MC Simulation
2071:
2069:
2066:
2064:
2061:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2038:
2034:
2033:Black–Scholes
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2015:
2013:
2011:
2007:
2000:
1996:
1992:
1989:
1987:
1986:Risk reversal
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1967:
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1916:Credit spread
1914:
1912:
1909:
1907:
1904:
1902:
1899:
1897:
1894:
1892:
1889:
1887:
1884:
1882:
1879:
1878:
1876:
1874:
1870:
1864:
1861:
1859:
1856:
1854:
1851:
1848:
1846:
1843:
1841:
1840:Interest rate
1838:
1836:
1835:Forward start
1833:
1831:
1828:
1826:
1823:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1787:
1785:
1783:
1779:
1773:
1770:
1768:
1765:
1763:
1762:Option styles
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1724:
1722:
1720:
1716:
1710:
1707:
1705:
1702:
1700:
1697:
1695:
1692:
1690:
1687:
1685:
1682:
1680:
1679:Open interest
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1659:Delta neutral
1657:
1656:
1654:
1650:
1647:
1645:
1641:
1637:
1632:
1628:
1621:
1616:
1614:
1609:
1607:
1602:
1601:
1598:
1580:
1576:
1570:
1567:
1555:
1551:
1545:
1542:
1529:
1525:
1518:
1515:
1511:
1507:
1501:
1498:
1491:
1489:
1487:
1483:
1479:
1474:
1472:
1468:
1464:
1460:
1451:
1446:
1430:
1422:
1419:
1403:
1396:
1379:
1375:
1367:
1364:
1346:
1342:
1334:
1316:
1299:
1284:
1277:
1260:
1256:
1248:
1247:
1230:
1225:
1222:
1217:
1213:
1209:
1204:
1200:
1192:
1173:
1168:
1163:
1157:
1153:
1147:
1143:
1139:
1134:
1130:
1126:
1121:
1117:
1110:
1104:
1100:
1094:
1090:
1083:
1080:
1074:
1069:
1065:
1057:
1056:
1055:
1054:where :
1032:
1028:
1024:
1009:
1004:
1000:
996:
992:
986:
982:
978:
970:
966:
962:
947:
942:
938:
934:
930:
926:
923:
920:
912:
911:
910:
888:
884:
868:
863:
859:
855:
851:
847:
844:
836:
832:
816:
811:
807:
803:
799:
793:
789:
785:
782:
775:
774:
773:
770:
753:
749:
740:
722:
718:
710:Suppose that
707:
705:
701:
697:
693:
689:
688:stock options
685:
677:
672:
669:
666:
665:
664:
661:
659:
655:
650:
648:
640:
620:
615:
613:
609:
605:
601:
597:
594:
586:
584:
570:
566:
562:
556:
528:
524:
519:
517:
513:
512:residual risk
510:To eliminate
508:
505:
498:
493:
478:
474:
470:
464:
456:
452:
449:
446:
442:
439:
436:
433:
429:
425:
421:
418:
415:
412:
411:Forward price
409:
406:
403:
400:
397:
394:
391:
388:
385:
382:
381:
377:
375:
371:
369:
365:
364:exchange rate
361:
357:
353:
349:
344:
342:
338:
337:exchange rate
330:
328:
326:
322:
318:
314:
310:
306:
302:
301:liquid market
297:
295:
291:
290:exchange rate
287:
283:
279:
275:
271:
259:
254:
252:
247:
245:
240:
239:
237:
236:
231:
228:
226:
223:
221:
220:Currency pair
218:
216:
215:Hard currency
213:
211:
208:
207:
206:
205:
200:
195:
194:Louvre Accord
192:
190:
187:
185:
182:
180:
177:
176:
175:
174:
169:
164:
161:
159:
158:Currency swap
156:
154:
151:
149:
146:
144:
141:
139:
136:
134:
131:
130:
129:
128:
123:
118:
115:
113:
110:
108:
105:
104:
103:
102:
97:
92:
89:
87:
84:
82:
79:
77:
74:
72:
69:
67:
66:Dollarization
64:
62:
59:
57:
54:
52:
51:Exchange rate
49:
47:
46:Currency band
44:
43:
42:
41:
36:
31:
19:
2279:Forward rate
2190:Total return
2078:Real options
1981:Ratio spread
1961:Naked option
1921:Debit spread
1756:
1752:Fixed income
1694:Strike price
1584:21 September
1582:. Retrieved
1578:
1569:
1559:21 September
1557:. Retrieved
1553:
1544:
1532:. Retrieved
1527:
1517:
1500:
1486:counterparty
1475:
1455:
1053:
908:
771:
708:
694:for certain
681:
662:
657:
653:
651:
616:
611:
607:
603:
599:
595:
590:
522:
520:
515:
509:
506:
502:
431:
427:
423:
399:Strike price
372:
367:
363:
359:
345:
341:strike price
334:
298:
277:
273:
269:
267:
189:Plaza Accord
162:
2210:Zero Coupon
2140:Correlation
2088:Vanna–Volga
1946:Iron condor
1732:Bond option
692:Black model
643:US$ 100,000
631:US$ 100,000
623:US$ 100,000
547:= $ 100,000
536:$ 2,000,000
531:.10 ×
384:Call option
368:USDGBP call
2519:Categories
2484:Tax policy
2200:Volatility
2110:Amortising
1951:Jelly roll
1886:Box spread
1881:Backspread
1873:Strategies
1709:Volatility
1704:the Greeks
1669:Expiration
1492:References
1445:volatility
704:log-normal
682:As in the
617:Suppose a
405:Spot price
390:Put option
360:GBPUSD put
282:derivative
2175:Inflation
2125:Commodity
2083:Trinomial
2018:Bachelier
2010:Valuation
1891:Butterfly
1825:Commodore
1674:Moneyness
1431:σ
1226:σ
1223:−
1169:σ
1144:σ
1127:−
1084:
1025:−
997:−
979:−
963:−
935:−
856:−
845:−
804:−
706:process.
608:uncertain
596:uncertain
560:↦
527:numéraire
468:↦
445:numéraire
438:Numéraire
315:, or the
274:FX option
2314:Slippage
2244:Contango
2228:Forwards
2195:Variance
2155:Dividend
2150:Currency
2063:Margrabe
2058:Lattices
2037:equation
2023:Binomial
1971:Strangle
1966:Straddle
1863:Swaption
1845:Lookback
1830:Compound
1772:Warrants
1747:European
1727:American
1719:Vanillas
1684:Pin risk
1664:Exercise
1530:. Farhan
690:and the
654:opposite
604:forwards
542:$ 2.0000
417:Notional
356:sterling
286:currency
202:See also
133:Currency
2233:Futures
1853:Rainbow
1820:Cliquet
1815:Chooser
1795:Barrier
1782:Exotics
1644:Options
1534:10 June
1443:is the
737:is the
612:options
600:certain
587:Hedging
545:
533:
516:foreign
499:Trading
432:forward
331:Example
280:) is a
99:Markets
2294:Margin
2160:Equity
2053:Heston
1956:Ladder
1906:Condor
1901:Collar
1858:Spread
1805:Binary
1800:Basket
1459:Greeks
606:, and
453:– the
424:strike
125:Assets
2165:Forex
2120:Basis
2115:Asset
2102:Swaps
2028:Black
1931:Fence
1790:Asian
1652:Terms
593:hedge
378:Terms
339:, or
1999:Bull
1995:Bear
1737:Call
1586:2016
1561:2016
1536:2023
1480:and
1478:SABR
1469:and
1423:and
1365:rate
686:for
635:US$
627:US$
523:rate
428:spot
348:call
1767:Put
658:not
430:or
354:on
352:put
276:or
2521::
1997:,
1757:FX
1577:.
1552:.
1526:.
1473:.
1081:ln
614:.
370:.
311:,
296:.
2039:)
2035:(
2001:)
1993:(
1619:e
1612:t
1605:v
1588:.
1563:.
1538:.
1504:"
1420:)
1404:T
1380:f
1376:r
1347:d
1343:r
1320:)
1317:x
1314:(
1309:N
1285:K
1261:0
1257:S
1231:T
1218:1
1214:d
1210:=
1205:2
1201:d
1174:T
1164:T
1161:)
1158:2
1154:/
1148:2
1140:+
1135:f
1131:r
1122:d
1118:r
1114:(
1111:+
1108:)
1105:K
1101:/
1095:0
1091:S
1087:(
1075:=
1070:1
1066:d
1038:)
1033:1
1029:d
1022:(
1017:N
1010:T
1005:f
1001:r
993:e
987:0
983:S
976:)
971:2
967:d
960:(
955:N
948:T
943:d
939:r
931:e
927:K
924:=
921:p
894:)
889:2
885:d
881:(
876:N
869:T
864:d
860:r
852:e
848:K
842:)
837:1
833:d
829:(
824:N
817:T
812:f
808:r
800:e
794:0
790:S
786:=
783:c
754:f
750:r
723:d
719:r
571:x
567:/
563:1
557:x
539:/
491:.
479:x
475:/
471:1
465:x
447:.
434:.
257:e
250:t
243:v
20:)
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