Time-changed geometric fractional Brownian motion and option pricing with transaction costs

Physica A: Statistical Mechanics and its Applications

Volumn 391, Issue 15, 2012, Pages 3971-3977

  Gu, Hui ^a   Liang, Jin Rong ^a   Zhang, Yun Xiu ^a,b  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b NANJING FORESTRY UNIVERSITY   (China)

Author keywords

Delta hedging; Inverse stable subordinator; Option pricing; Time changed process; Transaction costs

Indexed keywords

BROWNIAN MOVEMENT; ECONOMIC AND SOCIAL EFFECTS; ECONOMICS; FINANCIAL MARKETS; INVESTMENTS;

BLACK-SCHOLES MODEL; DELTA-HEDGING; FRACTIONAL BROWNIAN MOTION; OPTION PRICING; PRICING FORMULA; SELF-FINANCING; SUBORDINATORS; TRANSACTION COST;

COSTS;

EID: 84860530638     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2012.03.020     Document Type: Article

References (26)

1. F. Black, and M. Scholes The pricing of options and corporate liabilities Journal of Political Economy 81 1973 637 654
2. M. Magdziarz Black-Scholes formula in subdiffusive regime Journal of Statistical Physics 136 2009 553 564
3. E. Scalas, R. Gorenflo, and F. Mainardi Fractional calculus and continuous-time finance Physica A 284 2000 376 384
4. F. Mainardi, M. Raberto, R. Gorenflo, and E. Scalas Fractional calculus and continuous-time finance II: the waiting-time distribution Physica A 287 2000 468 481
5. S.C. Kou Stochastic modeling in nanoscale biophysics: subdiffusion within proteins Annals of Applied Statistics 2 2008 501 535
6. J. Janczura, and A. Wyomaska Subdynamics of financial data from fractional Fokker-Planck equation Acta Physica Polonica B 40 2009 1341 1351
7. S. Orzel, and A. Wyomaska Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times Journal of Statistical Physics 143 2011 447 454
8. J. Janczura, S. Orzel, and A. Wyomaska Subordinated α-stable Ornstein-Uhlenbeck process as a tool of financial data description Physica A 390 2011 4379 4387
9. P. Cheridito Arbitrage in fractional Brownian motion models Finance and Stochastics 7 4 2003 533 553
10. L.C.G. Rogers Arbitrage with fractional Brownian motion Mathematical Finance 7 1 1997 95 105
11. Xiao-Tian Wang Scaling and long-range dependence in option pricing I: pricing European option with transaction costs under the fractional Black-Scholes model Physica A 389 2010 438 444
12. M. Mastinsek Discrete-time delta hedging and the Black-Scholes model with transaction costs Mathematical Methods of Operations Research 64 2006 227 236
13. Xiao-Tian Wang, En-Hui Zhu, Ming-Ming Tang, and Hai-Gang Yan Scaling and long-range dependence in option pricing II: pricing European option with transaction costs under the mixed Brownian-fractional Brownian model Physica A 389 2010 445 451
14. Xiao-Tian Wang, Hai-Gang Yan, Ming-Ming Tang, and En-Hui Zhu Scaling and long-range dependence in option pricing III: a fractional version of the Merton model with transaction costs Physica A 389 2010 452 458
15. Xiao-Tian Wang Scaling and long range dependence in option pricing, IV: pricing European options with transaction costs under the multifractional Black-Scholes model Physica A 389 2010 789 796
16. J. Bertoin Lévy Processes 1996 Cambridge University Press Cambridge
17. K.I. Sato Processes and Infinitely Divisible Distributions 1999 Cambridge University Press Cambridge
18. A. Janicki, and A. Weron Simulation and Chaotic Behavior of α-Stable Stochastic Processes 1994 Dekker New York
19. A. Janicki, and A. Weron Can one see α-stable variables and processes Statistical Science 1994 109 126
20. A. Piryatinska, A.I. Saichev, and W.A. Woyczynski Models of anomalous diffusion: the subdiffusive case Physica A 349 2005 375 420
21. M. Magdziarz, and K. Weron Anomalous diffusion schemes underlying the Cole-Cole relaxation: the role of the inverse-time α-stable subordinator Physica A 367 2006 1 6
22. M. Magdziarz Stochastic representation of subdiffusion processes with time-dependent drift Stochastic Processes and their Applications 119 2009 3238 3252
23. M. Magdziarz Path properties of subdiffusion - a martingale approach Stochastic Models 26 2010 256 271
24. H.E. Leland Option pricing and replication with transactions costs The Journal of Finance 40 1985 1283 1301
25. A.N. Lageras A renewal-process-type expression for the moments of inverse subordinators Journal of Applied Probability 42 2005 1134 1144
26. S.G. Samko, A.A. Kilbas, and D.I. Maritchev Integrals and Derivatives of the Fractional Order and Some of their Applications 1993 Gordon and Breach Science Publishers Amsterdam