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142:, an example of a jump process and a generalization of the Poisson process in a different direction than that of CTMCs
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the article lacks a definition, illustrative examples, but is of importance (Poisson process, LĂ©vy process).
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118:, which states that the prices have large jumps interspersed with small continuous movements.
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model for pricing options assumes that the underlying instrument follows a traditional
73:, with random arrival times, rather than continuous movement, typically modelled as a
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136:(CTMC), an example of a jump process and a generalization of the Poisson process
170:
Tankov, P. (2003). Financial modelling with jump processes (Vol. 2). CRC press.
1564:
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1051:
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879:
66:
1005:
229:(1976). "Option pricing when underlying stock returns are discontinuous".
187:(1976). "The valuation of options for alternative stochastic processes".
100:, with continuous, random movements at all scales, no matter how small.
832:
Generalized autoregressive conditional heteroskedasticity (GARCH) model
272:
262:
85:
88:, various stochastic models are used to model the price movements of
276:
18:
812:
Autoregressive conditional heteroskedasticity (ARCH) model
340:
Independent and identically distributed random variables
1580:
108:
proposed that prices actually follow a 'jump process'.
817:
Autoregressive integrated moving average (ARIMA) model
152:
Kolmogorov equations (continuous-time Markov chains)
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114:extended this approach to a hybrid model known as
699:Stochastic chains with memory of variable length
1600:
288:
8:
69:process that has discrete movements, called
34:needs attention from an expert in statistics
1607:
1593:
827:Autoregressive–moving-average (ARMA) model
295:
281:
273:
16:Stochastic process with discrete movements
244:
202:
163:
1133:Doob's martingale convergence theorems
44:may be able to help recruit an expert.
885:Constant elasticity of variance (CEV)
875:Chan–Karolyi–Longstaff–Sanders (CKLS)
7:
1561:
1559:
1579:. You can help Knowledge (XXG) by
1372:Skorokhod's representation theorem
1153:Law of large numbers (weak/strong)
14:
1342:Martingale representation theorem
1563:
1387:Stochastic differential equation
1277:Doob's optional stopping theorem
1272:Doob–Meyer decomposition theorem
23:
1257:Convergence of random variables
1143:Fisher–Tippett–Gnedenko theorem
855:Binomial options pricing model
232:Journal of Financial Economics
190:Journal of Financial Economics
148:, an example of a jump process
130:, an example of a jump process
1:
1322:Kolmogorov continuity theorem
1158:Law of the iterated logarithm
1327:Kolmogorov extension theorem
1006:Generalized queueing network
514:Interacting particle systems
255:10.1016/0304-405X(76)90022-2
213:10.1016/0304-405X(76)90023-4
134:Continuous-time Markov chain
459:Continuous-time random walk
146:Interacting particle system
36:. The specific problem is:
1647:
1558:
1467:Extreme value theory (EVT)
1267:Doob decomposition theorem
559:Ornstein–Uhlenbeck process
330:Chinese restaurant process
1535:
1347:Optional stopping theorem
1148:Large deviation principle
900:Heath–Jarrow–Morton (HJM)
837:Moving-average (MA) model
822:Autoregressive (AR) model
647:Hidden Markov model (HMM)
581:Schramm–Loewner evolution
1262:Doléans-Dade exponential
1092:Progressively measurable
890:Cox–Ingersoll–Ross (CIR)
1482:Mathematical statistics
1472:Large deviations theory
1302:Infinitesimal generator
1163:Maximal ergodic theorem
1082:Piecewise-deterministic
684:Random dynamical system
549:Markov additive process
1575:-related article is a
1317:Karhunen–Loève theorem
1252:Cameron–Martin formula
1216:Burkholder–Davis–Gundy
611:Variance gamma process
42:WikiProject Statistics
1447:Actuarial mathematics
1409:Uniform integrability
1404:Stratonovich integral
1332:Lévy–Prokhorov metric
1236:Marcinkiewicz–Zygmund
1123:Central limit theorem
725:Gaussian random field
554:McKean–Vlasov process
474:Dyson Brownian motion
335:Galton–Watson process
90:financial instruments
1626:Stochastic processes
1522:Time series analysis
1477:Mathematical finance
1362:Reflection principle
689:Regenerative process
489:Fleming–Viot process
304:Stochastic processes
1517:Stochastic analysis
1357:Quadratic variation
1352:Prokhorov's theorem
1287:Feynman–Kac formula
757:Markov random field
405:Birth–death process
102:John Carrington Cox
1487:Probability theory
1367:Skorokhod integral
1337:Malliavin calculus
920:Korn-Kreer-Lenssen
804:Time series models
767:Pitman–Yor process
92:; for example the
1631:Probability stubs
1588:
1587:
1553:
1552:
1507:Signal processing
1226:Doob's upcrossing
1221:Doob's martingale
1185:Engelbert–Schmidt
1128:Donsker's theorem
1062:Feller-continuous
930:Rendleman–Bartter
720:Dirichlet process
637:Branching process
606:Telegraph process
499:Geometric process
479:Empirical process
469:Diffusion process
325:Branching process
320:Bernoulli process
98:diffusion process
59:
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1527:Machine learning
1414:Usual hypotheses
1297:Girsanov theorem
1282:Dynkin's formula
1047:Continuous paths
955:Actuarial models
895:Garman–Kohlhagen
865:Black–Karasinski
860:Black–Derman–Toy
847:Financial models
713:Fields and other
642:Gaussian process
591:Sigma-martingale
395:Additive process
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239:(1–2): 125–144.
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140:Counting process
112:Robert C. Merton
79:compound Poisson
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1492:Queueing theory
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1377:Skorokhod space
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1231:Kunita–Watanabe
1202:
1168:Sanov's theorem
1138:Ergodic theorem
1111:
1107:Time-reversible
1025:
988:Queueing models
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978:Sparre–Anderson
968:Cramér–Lundberg
949:
935:SABR volatility
841:
798:
750:Boolean network
708:
694:Renewal process
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574:Non-homogeneous
564:Poisson process
454:Contact process
417:Brownian motion
387:Continuous time
381:
375:Maximal entropy
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246:10.1.1.588.7328
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128:Poisson process
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1540:List of topics
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1399:Stopping time
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1173:Zero–one laws
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870:Black–Scholes
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772:Point process
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730:Gibbs measure
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519:ItĂ´ diffusion
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494:Gamma process
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350:Moran process
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312:Discrete time
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94:Black–Scholes
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65:is a type of
64:
53:
50:December 2013
43:
39:
35:
32:This article
30:
21:
20:
1581:expanding it
1570:
1555:
1457:Econometrics
1419:Wiener space
1307:ItĂ´ integral
1208:Inequalities
1097:Self-similar
1067:Gauss–Markov
1057:Exchangeable
1037:CĂ dlĂ g paths
973:Risk process
925:LIBOR market
794:Random graph
789:Random field
601:Superprocess
539:LĂ©vy process
534:Jump process
533:
509:Hunt process
345:Markov chain
236:
230:
221:
194:
188:
175:
166:
110:
106:Stephen Ross
83:
63:jump process
62:
60:
47:
37:
33:
1573:probability
1502:Ruin theory
1440:Disciplines
1312:ItĂ´'s lemma
1087:Predictable
762:Percolation
745:Potts model
740:Ising model
704:White noise
662:Differences
524:ItĂ´ process
464:Cox process
360:Loop-erased
355:Random walk
263:1721.1/1899
185:Ross, S. A.
1620:Categories
1512:Statistics
1292:Filtration
1193:Kolmogorov
1177:Blumenthal
1102:Stationary
1042:Continuous
1030:Properties
915:Hull–White
657:Martingale
544:Local time
432:Fractional
410:pure birth
181:Cox, J. C.
158:References
67:stochastic
1424:Classical
437:Geometric
427:Excursion
241:CiteSeerX
199:CiteSeerX
81:process.
1545:Category
1429:Abstract
963:BĂĽhlmann
569:Compound
122:See also
1052:Ergodic
940:VašĂÄŤek
782:Poisson
442:Meander
86:finance
1392:Tanaka
1077:Mixing
1072:Markov
945:Wilkie
910:Ho–Lee
905:Heston
677:Super-
422:Bridge
370:Biased
243:
201:
75:simple
1571:This
1245:Tools
1021:M/M/c
1016:M/M/1
1011:M/G/1
1001:Fluid
667:Local
71:jumps
1577:stub
1197:LĂ©vy
996:Bulk
880:Chen
672:Sub-
630:Both
104:and
777:Cox
259:hdl
251:doi
209:doi
84:In
77:or
1622::
1195:,
1191:,
1187:,
1183:,
1179:,
257:.
249:.
235:.
207:.
193:.
183:;
61:A
1608:e
1601:t
1594:v
1583:.
1199:)
1175:(
296:e
289:t
282:v
265:.
261::
253::
237:3
215:.
211::
195:3
52:)
48:(
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