419:, the option's strike price is fixed. The difference is that the option is not exercised at the price at maturity: the payoff is the maximum difference between the optimal underlying asset price and the strike. For the call option, the holder chooses to exercise at the point when the underlying asset price is at its highest level. For the put option, the holder chooses to exercise at the underlying asset's lowest price. The payoff functions for the lookback call and the lookback put, respectively, are given by:
40:
the call, the strike price is fixed at the asset's lowest price during the option's life, and, for the put, it is fixed at the asset's highest price. Note that these options are not really options, as they will be always exercised by their holder. In fact, the option is never out-of-the-money, which makes it more expensive than a standard option. The payoff functions for the lookback call and the lookback put, respectively, are given by:
3419:
1762:
2199:
1256:
39:
As the name introduces it, the option's strike price is floating and determined at maturity. The floating strike is the optimal value of the underlying asset's price during the option life. The payoff is the maximum difference between the market asset's price at maturity and the floating strike. For
2337:
Selecting specific dates is a more intricate way of creating partial lookback options and other partial path-dependent options. The principle lies in selecting a subset of monitoring dates, so that the lookback condition is less strong and thus reducing the premium. Examples include the partial
31:. The payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. The option allows the holder to "look back" over time to determine the payoff. There exist two kinds of lookback options: with floating strike and with fixed strike.
1552:
289:
2338:
lookback option proposed by Heynen and Kat, and the amnesiac lookback option proposed by Chang and Li. Discrete partial path-dependent options are overpriced under continuous assumptions; their pricing is complex and is typically performed using numerical methods.
1558:
1902:
962:
1386:
1891:
951:
578:
1392:
2332:
2209:
Partial lookback options are a subclass of lookback options with the same payoff structure, but with the goal of reducing its fair price. One way is to scale the fair price linearly with constant
46:
681:
model, and its notations, we can price the
European lookback options with floating strike. The pricing method is much more complicated than for the standard European options and can be found in
1757:{\displaystyle a_{3}(S,H)={\frac {\ln(S/H)-(r-{\frac {1}{2}}\sigma ^{2})\tau }{\sigma {\sqrt {\tau }}}}=a_{1}(S,H)-{\frac {2r{\sqrt {\tau }}}{\sigma }},{\text{ with }}H>0,S>0,}
2194:{\displaystyle LP_{t}=-S\Phi (-a_{1}(S,M))+Me^{-r\tau }\Phi (-a_{2}(S,M))+{\frac {S\sigma ^{2}}{2r}}(\Phi (a_{1}(S,M))-e^{-r\tau }(M/S)^{\frac {2r}{\sigma ^{2}}}\Phi (a_{3}(S,M))).}
1251:{\displaystyle LC_{t}=S\Phi (a_{1}(S,m))-me^{-r\tau }\Phi (a_{2}(S,m))-{\frac {S\sigma ^{2}}{2r}}(\Phi (-a_{1}(S,m))-e^{-r\tau }(m/S)^{\frac {2r}{\sigma ^{2}}}\Phi (-a_{3}(S,m))),}
2259:
1267:
738:
1797:
822:
2227:
830:
647:
614:
358:
325:
790:
764:
712:
1785:
385:
667:
405:
3256:
425:
3168:
2962:
2537:
1547:{\displaystyle a_{2}(S,H)={\frac {\ln(S/H)+(r-{\frac {1}{2}}\sigma ^{2})\tau }{\sigma {\sqrt {\tau }}}}=a_{1}(S,H)-\sigma {\sqrt {\tau }}}
2967:
2493:
Feng, Liming; Linetsky, Vadim (2009). "Computing exponential moments of the discrete maximum of a LĂ©vy process and lookback options".
2466:
Boyarchenko, Svetlana; Levendorski, Sergei (2013). "Efficient
Laplace inversion, Wiener-Hopf factorization and pricing lookbacks".
3302:
2992:
284:{\displaystyle LC_{float}=\max(S_{T}-S_{min},0)=S_{T}-S_{min},~~{\text{and}}~~LP_{float}=\max(S_{max}-S_{T},0)=S_{max}-S_{T},}
2363:
2267:
3124:
2860:
2406:
Heynen, Robert; Harry, Kat (1995). "Lookback options with discrete and partial monitoring of the underlying price".
3362:
2530:
1791:
3297:
2942:
3337:
2875:
2729:
2523:
2232:
1381:{\displaystyle a_{1}(S,H)={\frac {\ln(S/H)+(r+{\frac {1}{2}}\sigma ^{2})\tau }{\sigma {\sqrt {\tau }}}}}
3444:
3193:
3134:
2956:
3238:
3049:
3357:
3352:
1886:{\displaystyle \Phi (a)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{a}e^{-{\frac {x^{2}}{2}}}\,dx}
717:
3307:
3007:
2977:
2952:
2835:
2676:
2608:
946:{\displaystyle M=\max _{0\leq u\leq t}S_{u},~~m=\min _{0\leq u\leq t}S_{u}{\text{ and }}S_{t}=S.}
686:
3104:
3089:
3054:
2997:
795:
2212:
3317:
3084:
2982:
2661:
619:
586:
330:
297:
2379:
Conze, Antoine; Viswanathan (1991). "Path dependent options: The case of lookback options".
769:
743:
691:
3271:
3228:
3218:
3208:
3203:
2929:
2870:
2805:
2759:
2754:
2628:
2588:
2555:
2435:"The Amnesiac Lookback Option: Selectively Monitored Lookback Options and Cryptocurrencies"
1770:
363:
8:
3449:
3276:
3064:
2987:
2810:
3327:
3312:
3281:
3266:
3233:
3099:
2890:
2855:
2618:
2583:
2546:
2392:
652:
390:
573:{\displaystyle LC_{fix}=\max(S_{max}-K,0),~~{\text{and}}~~LP_{fix}=\max(K-S_{min},0),}
3332:
3322:
3261:
3248:
3223:
3109:
2895:
2691:
2359:
678:
3213:
3152:
3147:
3129:
3059:
2825:
2820:
2792:
2744:
2623:
2563:
2502:
2475:
2446:
2415:
2388:
1896:
Similarly, the price of the lookback put option with floating strike is given by:
3423:
3393:
3388:
3342:
3178:
3173:
3119:
3029:
2937:
2910:
2850:
2845:
2815:
2749:
2666:
2646:
1788:
416:
672:
3398:
3383:
3183:
3094:
3044:
3021:
3002:
2830:
2772:
2739:
2734:
2714:
2638:
2506:
2479:
2419:
956:
Then, the price of the lookback call option with floating strike is given by:
3438:
3378:
3347:
3188:
3114:
3074:
3069:
2905:
2777:
2724:
2719:
2701:
2598:
2578:
24:
2451:
2434:
3198:
2972:
2900:
2880:
2840:
2709:
2681:
2671:
2613:
28:
3079:
2947:
2918:
2914:
2865:
2656:
2651:
3403:
3039:
3034:
2800:
2686:
2593:
2515:
3163:
2885:
2782:
2603:
20:
649:
is the asset's minimum price during the life of the option, and
360:
is the asset's minimum price during the life of the option, and
3418:
792:, although the life of the option started at time zero. Define
673:
Arbitrage-free price of lookback options with floating strike
616:
is the asset's maximum price during the life of the option,
327:
is the asset's maximum price during the life of the option,
2468:
International
Journal of Theoretical and Applied Finance
34:
2465:
2354:
Musiela, Mark; Rutkowski, Marek (November 25, 2004).
2327:{\displaystyle \lambda (\max\{S_{i}\}_{1}^{T}-S_{T})}
2270:
2235:
2215:
1905:
1800:
1773:
1561:
1395:
1270:
965:
833:
798:
772:
746:
720:
694:
685:. Assume that there exists a continuously-compounded
655:
622:
589:
428:
393:
366:
333:
300:
49:
410:
2326:
2253:
2221:
2193:
1885:
1779:
1756:
1546:
1380:
1250:
945:
816:
784:
758:
732:
706:
661:
641:
608:
572:
399:
379:
352:
319:
283:
3436:
2378:
2353:
2277:
888:
841:
530:
451:
202:
78:
2439:Frontiers in Applied Mathematics and Statistics
27:with path dependency, among many other kind of
2531:
2492:
2294:
2280:
766:, and that we will price the option at time
387:is the underlying asset's price at maturity
2405:
2204:
2538:
2524:
2433:Chang, Ho-Chun Herbert; Li, Kevin (2018).
2450:
2356:Martingale Methods in Financial Modelling
1876:
3363:Power reverse dual-currency note (PRDC)
3303:Constant proportion portfolio insurance
2432:
3437:
2545:
740:. Assume that the time to maturity is
2519:
3298:Collateralized debt obligation (CDO)
35:Lookback option with floating strike
13:
2393:10.1111/j.1540-6261.1991.tb04648.x
2254:{\displaystyle 0<\lambda <1}
2151:
2057:
1987:
1928:
1839:
1801:
1774:
1205:
1108:
1041:
985:
714:and a constant stock's volatility
14:
3461:
411:Lookback option with fixed strike
3417:
1792:cumulative distribution function
3125:Year-on-year inflation-indexed
2486:
2459:
2426:
2399:
2372:
2347:
2321:
2274:
2185:
2182:
2179:
2167:
2154:
2125:
2110:
2088:
2085:
2073:
2060:
2054:
2021:
2018:
2006:
1990:
1962:
1959:
1947:
1931:
1810:
1804:
1694:
1682:
1648:
1619:
1613:
1599:
1584:
1572:
1528:
1516:
1482:
1453:
1447:
1433:
1418:
1406:
1357:
1328:
1322:
1308:
1293:
1281:
1242:
1239:
1236:
1224:
1208:
1179:
1164:
1142:
1139:
1127:
1111:
1105:
1072:
1069:
1057:
1044:
1016:
1013:
1001:
988:
564:
533:
485:
454:
243:
205:
119:
81:
1:
3135:Zero-coupon inflation-indexed
2341:
2408:Applied Mathematical Finance
733:{\displaystyle \sigma >0}
7:
3338:Foreign exchange derivative
2730:Callable bull/bear contract
10:
3466:
3412:
3371:
3290:
3247:
3239:Stock market index future
3143:
3020:
2928:
2791:
2700:
2637:
2571:
2562:
2553:
2507:10.1142/S0219024913500118
2480:10.1142/S0219024913500118
2420:10.1080/13504869500000014
817:{\displaystyle \tau =T-t}
3358:Mortgage-backed security
3353:Interest rate derivative
3328:Equity-linked note (ELN)
3313:Credit-linked note (CLN)
2222:{\displaystyle \lambda }
2205:Partial lookback options
19:, in the terminology of
3308:Contract for difference
2609:Risk-free interest rate
2495:Finance and Stochastics
2452:10.3389/fams.2018.00010
687:risk-free interest rate
642:{\displaystyle S_{min}}
609:{\displaystyle S_{max}}
353:{\displaystyle S_{min}}
320:{\displaystyle S_{max}}
3090:Forward Rate Agreement
2381:The Journal of Finance
2328:
2261:. Thus the payoff is:
2255:
2223:
2195:
1887:
1781:
1758:
1548:
1382:
1252:
947:
818:
786:
785:{\displaystyle t<T}
760:
759:{\displaystyle T>0}
734:
708:
707:{\displaystyle r>0}
663:
643:
610:
574:
401:
381:
354:
321:
285:
3318:Credit default option
2662:Employee stock option
2329:
2256:
2224:
2196:
1888:
1782:
1780:{\displaystyle \Phi }
1759:
1549:
1383:
1253:
948:
824:. Finally, set that
819:
787:
761:
735:
709:
669:is the strike price.
664:
644:
611:
575:
402:
382:
380:{\displaystyle S_{T}}
355:
322:
286:
3272:Inflation derivative
3257:Commodity derivative
3229:Single-stock futures
3219:Normal backwardation
3209:Interest rate future
3050:Conditional variance
2556:Derivative (finance)
2268:
2233:
2213:
1903:
1798:
1771:
1559:
1393:
1268:
963:
831:
796:
770:
744:
718:
692:
653:
620:
587:
426:
415:As for the standard
391:
364:
331:
298:
47:
3424:Business portal
3277:Property derivative
2307:
1848:
3282:Weather derivative
3267:Freight derivative
3249:Exotic derivatives
3169:Commodities future
2856:Intermarket spread
2619:Synthetic position
2547:Derivatives market
2324:
2293:
2251:
2219:
2191:
1883:
1831:
1777:
1754:
1544:
1378:
1248:
943:
908:
861:
814:
782:
756:
730:
704:
659:
639:
606:
570:
397:
377:
350:
317:
281:
3445:Options (finance)
3432:
3431:
3333:Equity derivative
3323:Credit derivative
3291:Other derivatives
3262:Energy derivative
3224:Perpetual futures
3105:Overnight indexed
3055:Constant maturity
3016:
3015:
2963:Finite difference
2896:Protective option
2365:978-3-540-20966-9
2148:
2052:
1872:
1829:
1828:
1728:
1720:
1714:
1667:
1664:
1636:
1542:
1501:
1498:
1470:
1376:
1373:
1345:
1202:
1103:
922:
887:
880:
877:
840:
662:{\displaystyle K}
507:
504:
500:
496:
493:
400:{\displaystyle T}
173:
170:
166:
162:
159:
3457:
3422:
3421:
3194:Forwards pricing
2968:Garman–Kohlhagen
2569:
2568:
2540:
2533:
2526:
2517:
2516:
2511:
2510:
2490:
2484:
2483:
2463:
2457:
2456:
2454:
2430:
2424:
2423:
2403:
2397:
2396:
2387:(5): 1893–1907.
2376:
2370:
2369:
2351:
2333:
2331:
2330:
2325:
2320:
2319:
2306:
2301:
2292:
2291:
2260:
2258:
2257:
2252:
2228:
2226:
2225:
2220:
2200:
2198:
2197:
2192:
2166:
2165:
2150:
2149:
2147:
2146:
2137:
2129:
2120:
2109:
2108:
2072:
2071:
2053:
2051:
2043:
2042:
2041:
2028:
2005:
2004:
1986:
1985:
1946:
1945:
1918:
1917:
1892:
1890:
1889:
1884:
1875:
1874:
1873:
1868:
1867:
1858:
1847:
1842:
1830:
1821:
1817:
1786:
1784:
1783:
1778:
1763:
1761:
1760:
1755:
1729:
1727: with
1726:
1721:
1716:
1715:
1710:
1701:
1681:
1680:
1668:
1666:
1665:
1660:
1654:
1647:
1646:
1637:
1629:
1609:
1591:
1571:
1570:
1553:
1551:
1550:
1545:
1543:
1538:
1515:
1514:
1502:
1500:
1499:
1494:
1488:
1481:
1480:
1471:
1463:
1443:
1425:
1405:
1404:
1387:
1385:
1384:
1379:
1377:
1375:
1374:
1369:
1363:
1356:
1355:
1346:
1338:
1318:
1300:
1280:
1279:
1257:
1255:
1254:
1249:
1223:
1222:
1204:
1203:
1201:
1200:
1191:
1183:
1174:
1163:
1162:
1126:
1125:
1104:
1102:
1094:
1093:
1092:
1079:
1056:
1055:
1040:
1039:
1000:
999:
978:
977:
952:
950:
949:
944:
933:
932:
923:
920:
918:
917:
907:
878:
875:
871:
870:
860:
823:
821:
820:
815:
791:
789:
788:
783:
765:
763:
762:
757:
739:
737:
736:
731:
713:
711:
710:
705:
668:
666:
665:
660:
648:
646:
645:
640:
638:
637:
615:
613:
612:
607:
605:
604:
579:
577:
576:
571:
557:
556:
526:
525:
505:
502:
501:
498:
494:
491:
472:
471:
447:
446:
417:European options
406:
404:
403:
398:
386:
384:
383:
378:
376:
375:
359:
357:
356:
351:
349:
348:
326:
324:
323:
318:
316:
315:
290:
288:
287:
282:
277:
276:
264:
263:
236:
235:
223:
222:
198:
197:
171:
168:
167:
164:
160:
157:
153:
152:
134:
133:
112:
111:
93:
92:
74:
73:
23:, are a type of
17:Lookback options
3465:
3464:
3460:
3459:
3458:
3456:
3455:
3454:
3435:
3434:
3433:
3428:
3416:
3408:
3394:Great Recession
3389:Government debt
3367:
3343:Fund derivative
3286:
3243:
3204:Futures pricing
3179:Dividend future
3174:Currency future
3157:
3139:
3012:
2988:Put–call parity
2924:
2911:Vertical spread
2846:Diagonal spread
2816:Calendar spread
2787:
2696:
2633:
2558:
2549:
2544:
2514:
2491:
2487:
2464:
2460:
2431:
2427:
2404:
2400:
2377:
2373:
2366:
2352:
2348:
2344:
2315:
2311:
2302:
2297:
2287:
2283:
2269:
2266:
2265:
2234:
2231:
2230:
2214:
2211:
2210:
2207:
2161:
2157:
2142:
2138:
2130:
2128:
2124:
2116:
2098:
2094:
2067:
2063:
2044:
2037:
2033:
2029:
2027:
2000:
1996:
1975:
1971:
1941:
1937:
1913:
1909:
1904:
1901:
1900:
1863:
1859:
1857:
1853:
1849:
1843:
1835:
1816:
1799:
1796:
1795:
1789:standard normal
1772:
1769:
1768:
1725:
1709:
1702:
1700:
1676:
1672:
1659:
1655:
1642:
1638:
1628:
1605:
1592:
1590:
1566:
1562:
1560:
1557:
1556:
1537:
1510:
1506:
1493:
1489:
1476:
1472:
1462:
1439:
1426:
1424:
1400:
1396:
1394:
1391:
1390:
1368:
1364:
1351:
1347:
1337:
1314:
1301:
1299:
1275:
1271:
1269:
1266:
1265:
1218:
1214:
1196:
1192:
1184:
1182:
1178:
1170:
1152:
1148:
1121:
1117:
1095:
1088:
1084:
1080:
1078:
1051:
1047:
1029:
1025:
995:
991:
973:
969:
964:
961:
960:
928:
924:
921: and
919:
913:
909:
891:
866:
862:
844:
832:
829:
828:
797:
794:
793:
771:
768:
767:
745:
742:
741:
719:
716:
715:
693:
690:
689:
675:
654:
651:
650:
627:
623:
621:
618:
617:
594:
590:
588:
585:
584:
546:
542:
515:
511:
497:
461:
457:
436:
432:
427:
424:
423:
413:
392:
389:
388:
371:
367:
365:
362:
361:
338:
334:
332:
329:
328:
305:
301:
299:
296:
295:
272:
268:
253:
249:
231:
227:
212:
208:
181:
177:
163:
142:
138:
129:
125:
101:
97:
88:
84:
57:
53:
48:
45:
44:
37:
12:
11:
5:
3463:
3453:
3452:
3447:
3430:
3429:
3427:
3426:
3413:
3410:
3409:
3407:
3406:
3401:
3399:Municipal debt
3396:
3391:
3386:
3384:Corporate debt
3381:
3375:
3373:
3369:
3368:
3366:
3365:
3360:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3315:
3310:
3305:
3300:
3294:
3292:
3288:
3287:
3285:
3284:
3279:
3274:
3269:
3264:
3259:
3253:
3251:
3245:
3244:
3242:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3206:
3201:
3196:
3191:
3186:
3184:Forward market
3181:
3176:
3171:
3166:
3160:
3158:
3156:
3155:
3150:
3144:
3141:
3140:
3138:
3137:
3132:
3127:
3122:
3117:
3112:
3107:
3102:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3065:Credit default
3062:
3057:
3052:
3047:
3042:
3037:
3032:
3026:
3024:
3018:
3017:
3014:
3013:
3011:
3010:
3005:
3000:
2995:
2990:
2985:
2980:
2975:
2970:
2965:
2960:
2950:
2945:
2940:
2934:
2932:
2926:
2925:
2923:
2922:
2908:
2903:
2898:
2893:
2888:
2883:
2878:
2873:
2868:
2863:
2861:Iron butterfly
2858:
2853:
2848:
2843:
2838:
2833:
2831:Covered option
2828:
2823:
2818:
2813:
2808:
2803:
2797:
2795:
2789:
2788:
2786:
2785:
2780:
2775:
2770:
2769:Mountain range
2767:
2762:
2757:
2752:
2747:
2742:
2737:
2732:
2727:
2722:
2717:
2712:
2706:
2704:
2698:
2697:
2695:
2694:
2689:
2684:
2679:
2674:
2669:
2664:
2659:
2654:
2649:
2643:
2641:
2635:
2634:
2632:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2586:
2581:
2575:
2573:
2566:
2560:
2559:
2554:
2551:
2550:
2543:
2542:
2535:
2528:
2520:
2513:
2512:
2501:(3): 1350011.
2485:
2474:(3): 1350011.
2458:
2425:
2414:(4): 273–284.
2398:
2371:
2364:
2345:
2343:
2340:
2335:
2334:
2323:
2318:
2314:
2310:
2305:
2300:
2296:
2290:
2286:
2282:
2279:
2276:
2273:
2250:
2247:
2244:
2241:
2238:
2218:
2206:
2203:
2202:
2201:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2169:
2164:
2160:
2156:
2153:
2145:
2141:
2136:
2133:
2127:
2123:
2119:
2115:
2112:
2107:
2104:
2101:
2097:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2070:
2066:
2062:
2059:
2056:
2050:
2047:
2040:
2036:
2032:
2026:
2023:
2020:
2017:
2014:
2011:
2008:
2003:
1999:
1995:
1992:
1989:
1984:
1981:
1978:
1974:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1949:
1944:
1940:
1936:
1933:
1930:
1927:
1924:
1921:
1916:
1912:
1908:
1882:
1879:
1871:
1866:
1862:
1856:
1852:
1846:
1841:
1838:
1834:
1827:
1824:
1820:
1815:
1812:
1809:
1806:
1803:
1776:
1765:
1764:
1753:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1724:
1719:
1713:
1708:
1705:
1699:
1696:
1693:
1690:
1687:
1684:
1679:
1675:
1671:
1663:
1658:
1653:
1650:
1645:
1641:
1635:
1632:
1627:
1624:
1621:
1618:
1615:
1612:
1608:
1604:
1601:
1598:
1595:
1589:
1586:
1583:
1580:
1577:
1574:
1569:
1565:
1554:
1541:
1536:
1533:
1530:
1527:
1524:
1521:
1518:
1513:
1509:
1505:
1497:
1492:
1487:
1484:
1479:
1475:
1469:
1466:
1461:
1458:
1455:
1452:
1449:
1446:
1442:
1438:
1435:
1432:
1429:
1423:
1420:
1417:
1414:
1411:
1408:
1403:
1399:
1388:
1372:
1367:
1362:
1359:
1354:
1350:
1344:
1341:
1336:
1333:
1330:
1327:
1324:
1321:
1317:
1313:
1310:
1307:
1304:
1298:
1295:
1292:
1289:
1286:
1283:
1278:
1274:
1259:
1258:
1247:
1244:
1241:
1238:
1235:
1232:
1229:
1226:
1221:
1217:
1213:
1210:
1207:
1199:
1195:
1190:
1187:
1181:
1177:
1173:
1169:
1166:
1161:
1158:
1155:
1151:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1124:
1120:
1116:
1113:
1110:
1107:
1101:
1098:
1091:
1087:
1083:
1077:
1074:
1071:
1068:
1065:
1062:
1059:
1054:
1050:
1046:
1043:
1038:
1035:
1032:
1028:
1024:
1021:
1018:
1015:
1012:
1009:
1006:
1003:
998:
994:
990:
987:
984:
981:
976:
972:
968:
954:
953:
942:
939:
936:
931:
927:
916:
912:
906:
903:
900:
897:
894:
890:
886:
883:
874:
869:
865:
859:
856:
853:
850:
847:
843:
839:
836:
813:
810:
807:
804:
801:
781:
778:
775:
755:
752:
749:
729:
726:
723:
703:
700:
697:
674:
671:
658:
636:
633:
630:
626:
603:
600:
597:
593:
581:
580:
569:
566:
563:
560:
555:
552:
549:
545:
541:
538:
535:
532:
529:
524:
521:
518:
514:
510:
490:
487:
484:
481:
478:
475:
470:
467:
464:
460:
456:
453:
450:
445:
442:
439:
435:
431:
412:
409:
396:
374:
370:
347:
344:
341:
337:
314:
311:
308:
304:
292:
291:
280:
275:
271:
267:
262:
259:
256:
252:
248:
245:
242:
239:
234:
230:
226:
221:
218:
215:
211:
207:
204:
201:
196:
193:
190:
187:
184:
180:
176:
156:
151:
148:
145:
141:
137:
132:
128:
124:
121:
118:
115:
110:
107:
104:
100:
96:
91:
87:
83:
80:
77:
72:
69:
66:
63:
60:
56:
52:
36:
33:
9:
6:
4:
3:
2:
3462:
3451:
3448:
3446:
3443:
3442:
3440:
3425:
3420:
3415:
3414:
3411:
3405:
3402:
3400:
3397:
3395:
3392:
3390:
3387:
3385:
3382:
3380:
3379:Consumer debt
3377:
3376:
3374:
3372:Market issues
3370:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3348:Fund of funds
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3295:
3293:
3289:
3283:
3280:
3278:
3275:
3273:
3270:
3268:
3265:
3263:
3260:
3258:
3255:
3254:
3252:
3250:
3246:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3189:Forward price
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3161:
3159:
3154:
3151:
3149:
3146:
3145:
3142:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3108:
3106:
3103:
3101:
3100:Interest rate
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3027:
3025:
3023:
3019:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2993:MC Simulation
2991:
2989:
2986:
2984:
2981:
2979:
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2958:
2954:
2953:Black–Scholes
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2935:
2933:
2931:
2927:
2920:
2916:
2912:
2909:
2907:
2906:Risk reversal
2904:
2902:
2899:
2897:
2894:
2892:
2889:
2887:
2884:
2882:
2879:
2877:
2874:
2872:
2869:
2867:
2864:
2862:
2859:
2857:
2854:
2852:
2849:
2847:
2844:
2842:
2839:
2837:
2836:Credit spread
2834:
2832:
2829:
2827:
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2802:
2799:
2798:
2796:
2794:
2790:
2784:
2781:
2779:
2776:
2774:
2771:
2768:
2766:
2763:
2761:
2760:Interest rate
2758:
2756:
2755:Forward start
2753:
2751:
2748:
2746:
2743:
2741:
2738:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2707:
2705:
2703:
2699:
2693:
2690:
2688:
2685:
2683:
2682:Option styles
2680:
2678:
2675:
2673:
2670:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2644:
2642:
2640:
2636:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2599:Open interest
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2579:Delta neutral
2577:
2576:
2574:
2570:
2567:
2565:
2561:
2557:
2552:
2548:
2541:
2536:
2534:
2529:
2527:
2522:
2521:
2518:
2508:
2504:
2500:
2496:
2489:
2481:
2477:
2473:
2469:
2462:
2453:
2448:
2444:
2440:
2436:
2429:
2421:
2417:
2413:
2409:
2402:
2394:
2390:
2386:
2382:
2375:
2367:
2361:
2357:
2350:
2346:
2339:
2316:
2312:
2308:
2303:
2298:
2288:
2284:
2271:
2264:
2263:
2262:
2248:
2245:
2242:
2239:
2236:
2216:
2188:
2176:
2173:
2170:
2162:
2158:
2143:
2139:
2134:
2131:
2121:
2117:
2113:
2105:
2102:
2099:
2095:
2091:
2082:
2079:
2076:
2068:
2064:
2048:
2045:
2038:
2034:
2030:
2024:
2015:
2012:
2009:
2001:
1997:
1993:
1982:
1979:
1976:
1972:
1968:
1965:
1956:
1953:
1950:
1942:
1938:
1934:
1925:
1922:
1919:
1914:
1910:
1906:
1899:
1898:
1897:
1894:
1880:
1877:
1869:
1864:
1860:
1854:
1850:
1844:
1836:
1832:
1825:
1822:
1818:
1813:
1807:
1793:
1790:
1751:
1748:
1745:
1742:
1739:
1736:
1733:
1730:
1722:
1717:
1711:
1706:
1703:
1697:
1691:
1688:
1685:
1677:
1673:
1669:
1661:
1656:
1651:
1643:
1639:
1633:
1630:
1625:
1622:
1616:
1610:
1606:
1602:
1596:
1593:
1587:
1581:
1578:
1575:
1567:
1563:
1555:
1539:
1534:
1531:
1525:
1522:
1519:
1511:
1507:
1503:
1495:
1490:
1485:
1477:
1473:
1467:
1464:
1459:
1456:
1450:
1444:
1440:
1436:
1430:
1427:
1421:
1415:
1412:
1409:
1401:
1397:
1389:
1370:
1365:
1360:
1352:
1348:
1342:
1339:
1334:
1331:
1325:
1319:
1315:
1311:
1305:
1302:
1296:
1290:
1287:
1284:
1276:
1272:
1264:
1263:
1262:
1245:
1233:
1230:
1227:
1219:
1215:
1211:
1197:
1193:
1188:
1185:
1175:
1171:
1167:
1159:
1156:
1153:
1149:
1145:
1136:
1133:
1130:
1122:
1118:
1114:
1099:
1096:
1089:
1085:
1081:
1075:
1066:
1063:
1060:
1052:
1048:
1036:
1033:
1030:
1026:
1022:
1019:
1010:
1007:
1004:
996:
992:
982:
979:
974:
970:
966:
959:
958:
957:
940:
937:
934:
929:
925:
914:
910:
904:
901:
898:
895:
892:
884:
881:
872:
867:
863:
857:
854:
851:
848:
845:
837:
834:
827:
826:
825:
811:
808:
805:
802:
799:
779:
776:
773:
753:
750:
747:
727:
724:
721:
701:
698:
695:
688:
684:
680:
679:Black–Scholes
670:
656:
634:
631:
628:
624:
601:
598:
595:
591:
567:
561:
558:
553:
550:
547:
543:
539:
536:
527:
522:
519:
516:
512:
508:
488:
482:
479:
476:
473:
468:
465:
462:
458:
448:
443:
440:
437:
433:
429:
422:
421:
420:
418:
408:
394:
372:
368:
345:
342:
339:
335:
312:
309:
306:
302:
278:
273:
269:
265:
260:
257:
254:
250:
246:
240:
237:
232:
228:
224:
219:
216:
213:
209:
199:
194:
191:
188:
185:
182:
178:
174:
154:
149:
146:
143:
139:
135:
130:
126:
122:
116:
113:
108:
105:
102:
98:
94:
89:
85:
75:
70:
67:
64:
61:
58:
54:
50:
43:
42:
41:
32:
30:
26:
25:exotic option
22:
18:
3199:Forward rate
3110:Total return
2998:Real options
2901:Ratio spread
2881:Naked option
2841:Debit spread
2764:
2672:Fixed income
2614:Strike price
2498:
2494:
2488:
2471:
2467:
2461:
2442:
2438:
2428:
2411:
2407:
2401:
2384:
2380:
2374:
2358:. Springer.
2355:
2349:
2336:
2208:
1895:
1766:
1260:
955:
682:
676:
582:
414:
293:
38:
16:
15:
3130:Zero Coupon
3060:Correlation
3008:Vanna–Volga
2866:Iron condor
2652:Bond option
3450:Investment
3439:Categories
3404:Tax policy
3120:Volatility
3030:Amortising
2871:Jelly roll
2806:Box spread
2801:Backspread
2793:Strategies
2629:Volatility
2624:the Greeks
2589:Expiration
2342:References
1767:and where
677:Using the
3095:Inflation
3045:Commodity
3003:Trinomial
2938:Bachelier
2930:Valuation
2811:Butterfly
2745:Commodore
2594:Moneyness
2309:−
2272:λ
2243:λ
2217:λ
2152:Φ
2140:σ
2106:τ
2100:−
2092:−
2058:Φ
2035:σ
1994:−
1988:Φ
1983:τ
1977:−
1935:−
1929:Φ
1923:−
1855:−
1840:∞
1837:−
1833:∫
1826:π
1802:Φ
1775:Φ
1718:σ
1712:τ
1698:−
1662:τ
1657:σ
1652:τ
1640:σ
1626:−
1617:−
1597:
1540:τ
1535:σ
1532:−
1496:τ
1491:σ
1486:τ
1474:σ
1460:−
1431:
1371:τ
1366:σ
1361:τ
1349:σ
1306:
1212:−
1206:Φ
1194:σ
1160:τ
1154:−
1146:−
1115:−
1109:Φ
1086:σ
1076:−
1042:Φ
1037:τ
1031:−
1020:−
986:Φ
902:≤
896:≤
855:≤
849:≤
809:−
800:τ
722:σ
540:−
474:−
266:−
225:−
136:−
95:−
3234:Slippage
3164:Contango
3148:Forwards
3115:Variance
3075:Dividend
3070:Currency
2983:Margrabe
2978:Lattices
2957:equation
2943:Binomial
2891:Strangle
2886:Straddle
2783:Swaption
2765:Lookback
2750:Compound
2692:Warrants
2667:European
2647:American
2639:Vanillas
2604:Pin risk
2584:Exercise
2229:, where
3153:Futures
2773:Rainbow
2740:Cliquet
2735:Chooser
2715:Barrier
2702:Exotics
2564:Options
1787:is the
1261:where
683:Musiela
29:options
21:finance
3214:Margin
3080:Equity
2973:Heston
2876:Ladder
2826:Condor
2821:Collar
2778:Spread
2725:Binary
2720:Basket
2362:
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583:where
506:
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294:where
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158:
3085:Forex
3040:Basis
3035:Asset
3022:Swaps
2948:Black
2851:Fence
2710:Asian
2572:Terms
2919:Bull
2915:Bear
2657:Call
2360:ISBN
2246:<
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1734:>
777:<
751:>
725:>
699:>
2687:Put
2503:doi
2476:doi
2447:doi
2416:doi
2389:doi
2278:max
889:min
842:max
531:max
499:and
452:max
203:max
165:and
79:max
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