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Volumn 136, Issue 3, 2009, Pages 553-564

Black-scholes formula in subdiffusive regime

Author keywords

Black Scholes formula; Fractional Fokker Planck equation; Subdiffusion

Indexed keywords


EID: 70349309658     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9791-4     Document Type: Article
Times cited : (94)

References (30)
  • 1
    • 0003029969 scopus 로고
    • Théorie de la spéculation
    • Bachelier, L.: Théorie de la spéculation. Ann. Ec. Norm. Supér. 17, 21-86 (1900)
    • (1900) Ann. Ec. Norm. SupéR. , vol.17 , pp. 21-86
    • Bachelier, L.1
  • 2
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • Barkai, E., Metzler, R., Klafter, J.: From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E 61, 132-138 (2000)
    • (2000) Phys. Rev. E , vol.61 , pp. 132-138
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 3
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637-659 (1973)
    • (1973) J. Polit. Econ. , vol.81 , pp. 637-659
    • Black, F.1    Scholes, M.2
  • 5
    • 0347526221 scopus 로고    scopus 로고
    • Spatial gliding, temporal trapping, and anomalous transport
    • Eliazar, I., Klafter, J.: Spatial gliding, temporal trapping, and anomalous transport. Physica D 187, 30-50 (2004)
    • (2004) Physica D , vol.187 , pp. 30-50
    • Eliazar, I.1    Klafter, J.2
  • 6
    • 0036642610 scopus 로고    scopus 로고
    • Analytical representations for relaxation functions of glasses
    • Hilfer, R.: Analytical representations for relaxation functions of glasses. J. Non-Cryst. Solids 305, 122-126 (2002)
    • (2002) J. Non-Cryst. Solids , vol.305 , pp. 122-126
    • Hilfer, R.1
  • 8
    • 67649090532 scopus 로고    scopus 로고
    • Subdynamics of financial data from fractional Fokker-Planck equation
    • Janczura, J., Wylomanska, A.: Subdynamics of financial data from fractional Fokker-Planck equation. Acta Phys. Pol. B 40, 1341-1351 (2009)
    • (2009) Acta Phys. Pol. B , vol.40 , pp. 1341-1351
    • Janczura, J.1    Wylomanska, A.2
  • 10
    • 69749117030 scopus 로고    scopus 로고
    • Stochastic representation of subdiffusion processes with time-dependent drift
    • doi:10.1016/j.spa.2009.05.006
    • Magdziarz, M.: Stochastic representation of subdiffusion processes with time-dependent drift. Stoch. Proc. Appl. (2009). doi:10.1016/j.spa.2009.05.006
    • (2009) Stoch. Proc. Appl.
    • Magdziarz, M.1
  • 11
    • 85204067722 scopus 로고    scopus 로고
    • Magdziarz, M.: Path properties of subdiffusion-a martingale approach (2009, submitted)
    • Magdziarz, M.: Path properties of subdiffusion-a martingale approach (2009, submitted)
  • 12
    • 67650581750 scopus 로고    scopus 로고
    • Langevin picture of subdiffusion with infinitely divisible waiting times
    • Magdziarz, M.: Langevin picture of subdiffusion with infinitely divisible waiting times. J. Stat. Phys. 135, 763-772 (2009)
    • (2009) J. Stat. Phys. , vol.135 , pp. 763-772
    • Magdziarz, M.1
  • 13
    • 56849094437 scopus 로고    scopus 로고
    • Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: The case of a time-dependent force
    • Magdziarz, M., Weron, A., Klafter, J.: Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: the case of a time-dependent force. Phys. Rev. Lett. 101, 210601 (2008)
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 210601
    • Magdziarz, M.1    Weron, A.2    Klafter, J.3
  • 14
    • 33846621507 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation
    • Magdziarz, M., Weron, A., Weron, K.: Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation. Phys. Rev. E 75, 016708 (2007)
    • (2007) Phys. Rev. E , vol.75 , pp. 016708
    • Magdziarz, M.1    Weron, A.2    Weron, K.3
  • 16
  • 17
    • 0015602539 scopus 로고
    • Theory of rational option pricing
    • Merton, R.C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4, 141-183 (1973)
    • (1973) Bell J. Econ. Manag. Sci. , vol.4 , pp. 141-183
    • Merton, R.C.1
  • 18
    • 18144408075 scopus 로고    scopus 로고
    • Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach
    • Metzler, R., Barkai, E., Klafter, J.: Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82, 3563-3567 (1999)
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 3563-3567
    • Metzler, R.1    Barkai, E.2    Klafter, J.3
  • 19
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R., Klafter, J.: The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1-77 (2000)
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 21
    • 13444309297 scopus 로고    scopus 로고
    • Models of anomalous diffusion: The subdiffusive case
    • Piryatinska, A., Saichev, A.I., Woyczynski, W.A.: Models of anomalous diffusion: the subdiffusive case. Physica A 349, 375-420 (2005)
    • (2005) Physica A , vol.349 , pp. 375-420
    • Piryatinska, A.1    Saichev, A.I.2    Woyczynski, W.A.3
  • 24
    • 0002677397 scopus 로고
    • Rational theory of warrant pricing
    • Samuelson, P.A.: Rational theory of warrant pricing. Ind. Manag. Rev. 6, 13-31 (1965)
    • (1965) Ind. Manag. Rev. , vol.6 , pp. 13-31
    • Samuelson, P.A.1
  • 26
    • 4243262854 scopus 로고    scopus 로고
    • Lévy flights from a continuous-time process
    • Sokolov, I.M.: Lévy flights from a continuous-time process. Phys. Rev. E 63, 011104 (2000)
    • (2000) Phys. Rev. E , vol.63 , pp. 011104
    • Sokolov, I.M.1
  • 27
    • 41349107351 scopus 로고    scopus 로고
    • Solutions of a class of non-Markovian Fokker-Planck equations
    • Sokolov, I.M.: Solutions of a class of non-Markovian Fokker-Planck equations. Phys. Rev. E 66, 041101 (2002)
    • (2002) Phys. Rev. E , vol.66 , pp. 041101
    • Sokolov, I.M.1
  • 28
    • 0037442596 scopus 로고    scopus 로고
    • Black-Scholes model under subordination
    • Stanislavsky, A.A.: Black-Scholes model under subordination. Physica A 318, 469-474 (2003)
    • (2003) Physica a , vol.318 , pp. 469-474
    • Stanislavsky, A.A.1
  • 29
    • 56649084847 scopus 로고    scopus 로고
    • Diffusion and relaxation controlled by tempered-stable processes
    • Stanislavsky, A.A., Weron, K., Weron, A.: Diffusion and relaxation controlled by tempered-stable processes. Phys. Rev. E 78, 051106 (2008)
    • (2008) Phys. Rev. E , vol.78 , pp. 051106
    • Stanislavsky, A.A.1    Weron, K.2    Weron, A.3
  • 30
    • 0030585552 scopus 로고    scopus 로고
    • On the Chambers-Mallows-Stuck method for simulating skewed stable random variables
    • Weron, R.: On the Chambers-Mallows-Stuck method for simulating skewed stable random variables. Stat. Probab. Lett. 28, 165-171 (1996)
    • (1996) Stat. Probab. Lett. , vol.28 , pp. 165-171
    • Weron, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.