메뉴 건너뛰기




Volumn 10, Issue 2, 2010, Pages 177-194

A comparison of biased simulation schemes for stochastic volatility models

Author keywords

Boundary behaviour; Cev process; Discretization; Euler maruyama; Heston; Square root process; Stochastic volatility; Strong convergence; Weak convergence

Indexed keywords


EID: 75849146031     PISSN: 14697688     EISSN: 14697696     Source Type: Journal    
DOI: 10.1080/14697680802392496     Document Type: Article
Times cited : (232)

References (45)
  • 1
    • 34547536758 scopus 로고    scopus 로고
    • On the discretization schemes for the CIR (and Bessel squared) processes
    • Alfonsi, A., On the discretization schemes for the CIR (and Bessel squared) processes. Monte Carlo Meth. Appl., 2005, 11, 355-384.
    • (2005) Monte Carlo Meth. Appl. , vol.11 , pp. 355-384
    • Alfonsi, A.1
  • 2
    • 70450057220 scopus 로고    scopus 로고
    • Simple and efficient simulation of the Heston stochastic volatility model
    • Andersen, L.B.G., Simple and efficient simulation of the Heston stochastic volatility model. J. Comput. Finan., 2008, 11, 1-42.
    • (2008) J. Comput. Finan. , vol.11 , pp. 1-42
    • Andersen, L.B.G.1
  • 3
    • 0142077325 scopus 로고    scopus 로고
    • Volatile volatilities
    • Andersen, L.B.G. and Andreasen, J., Volatile volatilities. Risk, 2002, 15, 163-168.
    • (2002) Risk , vol.15 , pp. 163-168
    • Andersen, L.B.G.1    Andreasen, J.2
  • 4
    • 33845958424 scopus 로고    scopus 로고
    • Extended LIBOR market models with stochastic volatility
    • Andersen, L.B.G. and Brotherton-Ratcliffe, R., Extended LIBOR market models with stochastic volatility. J. Comput. Finan., 2005, 9, 1-40.
    • (2005) J. Comput. Finan. , vol.9 , pp. 1-40
    • Andersen, L.B.G.1    Brotherton-Ratcliffe, R.2
  • 5
    • 33845957927 scopus 로고    scopus 로고
    • Moment explosions in stochastic volatility models
    • Andersen, L.B.G. and Piterbarg, V.V., Moment explosions in stochastic volatility models. Finan. Stochast., 2007, 11, 29-50.
    • (2007) Finan. Stochast. , vol.11 , pp. 29-50
    • Andersen, L.B.G.1    Piterbarg, V.V.2
  • 6
    • 0030534228 scopus 로고    scopus 로고
    • Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options
    • Bates, D.S., Jumps and stochastic volatility: exchange rate processes implicit in Deutsche Mark options. Rev. Finan. Stud., 1996, 9, 69-107.
    • (1996) Rev. Finan. Stud. , vol.9 , pp. 69-107
    • Bates, D.S.1
  • 7
    • 62749153463 scopus 로고    scopus 로고
    • Euler scheme for SDEs with non-Lipschitz diffusion coefficient: Strong convergence
    • Berkaoui, A., Bossy, M. and Diop, A., Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence. ESAIM Probab. Stat., 2008, 12, 1-11.
    • (2008) ESAIM Probab. Stat. , vol.12 , pp. 1-11
    • Berkaoui, A.1    Bossy, M.2    Diop, A.3
  • 9
    • 17744385797 scopus 로고    scopus 로고
    • Exact simulation of option Greeks under stochastic volatility and jump diffusion models
    • edited by R.G. Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters, (The Society for Computer Simulation)
    • Broadie, M. and Kaya, Ö., Exact simulation of option Greeks under stochastic volatility and jump diffusion models, in Proceedings of the 2004 Winter Simulation Conference, edited by R.G. Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters, pp. 1607-1615, 2004 (The Society for Computer Simulation).
    • (2004) Proceedings of The 2004 Winter Simulation Conference , pp. 1607-1615
    • Broadie, M.1    Kaya, O.2
  • 10
    • 33645556341 scopus 로고    scopus 로고
    • Exact simulation of stochastic volatility and other affine jump diffusion processes
    • Broadie, M. and Kaya, Ö., Exact simulation of stochastic volatility and other affine jump diffusion processes. Operat. Res., 2006, 54, 217-231.
    • (2006) Operat. Res. , vol.54 , pp. 217-231
    • Broadie, M.1    Kaya, O.2
  • 12
    • 0002488565 scopus 로고    scopus 로고
    • Option valuation using the fast Fourier transform
    • Carr, P. and Madan, D.B., Option valuation using the fast Fourier transform. J. Comput. Finan., 1999, 2, 61-73.
    • (1999) J. Comput. Finan. , vol.2 , pp. 61-73
    • Carr, P.1    Madan, D.B.2
  • 13
    • 4944226107 scopus 로고    scopus 로고
    • Which GARCH model for option valuation?
    • Christoffersen, P. and Jacobs, K., Which GARCH model for option valuation? Manag. Sci., 2004, 50, 1204-1221.
    • (2004) Manag. Sci. , vol.50 , pp. 1204-1221
    • Christoffersen, P.1    Jacobs, K.2
  • 14
    • 0001205798 scopus 로고
    • A theory of the term structure of interest rates
    • Cox, J.C., Ingersoll, J.E. and Ross, S.A., A theory of the term structure of interest rates. Econometrica, 1985, 53, 385-407.
    • (1985) Econometrica , vol.53 , pp. 385-407
    • Cox, J.C.1    Ingersoll, J.E.2    Ross, S.A.3
  • 15
    • 0032026704 scopus 로고    scopus 로고
    • Convergence of discretized stochastic (interest rate) processes with stochastic drift term
    • Deelstra, G. and Delbaen, F., Convergence of discretized stochastic (interest rate) processes with stochastic drift term. Appl. Stochast. Models Data Anal., 1998, 14, 77-84.
    • (1998) Appl. Stochast. Models Data Anal. , vol.14 , pp. 77-84
    • Deelstra, G.1    Delbaen, F.2
  • 17
    • 18044367726 scopus 로고    scopus 로고
    • Integration ofLangevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions
    • Dornic, I., Chaté, H. and Muñoz, M.A., Integration ofLangevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions. Phys. Rev.Lett., 2005, 94, 100601-1-100601-4.
    • (2005) Phys. Rev.lett. , vol.94 , pp. 1-4
    • Dornic, I.1    Chaté, H.2    Muñoz, M.A.3
  • 18
    • 21344444681 scopus 로고
    • Efficient Monte Carlo simulation ofsecurity prices
    • Duffie, D. and Glynn, P., Efficient Monte Carlo simulation ofsecurity prices. Ann. Appl. Probab., 1995, 5, 897-905.
    • (1995) Ann. Appl. Probab. , vol.5 , pp. 897-905
    • Duffie, D.1    Glynn, P.2
  • 19
    • 0001668150 scopus 로고    scopus 로고
    • K., Transform analysis and asset pricing for affine jump-diffusions
    • Duffie, D., Pan, J. and K. Singleton, K., Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 2000, 68, 1343-1376.
    • (2000) Econometrica , vol.68 , pp. 1343-1376
    • Duffie, D.1    Pan, J.2    Singleton, K.3
  • 21
    • 0001277826 scopus 로고
    • Two singular diffusion problems
    • Feller, W., Two singular diffusion problems. Ann. Math., 1951, 54, 173-182.
    • (1951) Ann. Math. , vol.54 , pp. 173-182
    • Feller, W.1
  • 24
    • 0043228001 scopus 로고    scopus 로고
    • A note on Euler approximations
    • Gyöngy, L., A note on Euler approximations. Potential Anal., 1998, 8, 205-216.
    • (1998) Potential Anal , vol.8 , pp. 205-216
    • Gyö, L.1
  • 26
    • 0037836721 scopus 로고
    • A closed-form solution for options with stochastic volatility with applications to bond and currency options
    • Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Finan. Stud., 1993, 6, 327-343.
    • (1993) Rev. Finan. Stud. , vol.6 , pp. 327-343
    • Heston, S.L.1
  • 27
    • 0034375561 scopus 로고    scopus 로고
    • A closed-form GARCH option valuation model
    • Heston, S.L. and Nandi, S., A closed-form GARCH option valuation model. Rev. Finan. Stud., 2000, 13, 585-625.
    • (2000) Rev. Finan. Stud. , vol.13 , pp. 585-625
    • Heston, S.L.1    Nandi, S.2
  • 28
    • 33749566186 scopus 로고    scopus 로고
    • Convergence of the Monte Carlo simulations involving the mean-reverting square root process
    • Higham, D.J. and Mao, X., Convergence of the Monte Carlo simulations involving the mean-reverting square root process. J. Comput. Finan., 2005, 8, 35-62.
    • (2005) J. Comput. Finan. , vol.8 , pp. 35-62
    • Higham, D.J.1    Mao, X.2
  • 30
    • 75849153938 scopus 로고    scopus 로고
    • Stochastic volatility models: Past, present and future
    • edited by P. Wilmott, (Wiley: New York)
    • Jäckel, P., Stochastic volatility models: past, present and future, in The Best of Wilmott 1: Incorporating the Quantitative Finance Review, edited by P. Wilmott, pp. 379-390, 2004 (Wiley: New York).
    • (2004) The Best of Wilmott 1: Incorporating the Quantitative Finance Review , pp. 379-390
    • Jäckel, P.1
  • 32
    • 33751534524 scopus 로고    scopus 로고
    • Fast strong approximation Monte- Carlo schemes for stochastic volatility models
    • Kahl, C. and Jäckel, P., Fast strong approximation Monte- Carlo schemes for stochastic volatility models. Quant. Finan., 2006, 6, 513-536.
    • (2006) Quant. Finan. , vol.6 , pp. 513-536
    • Kahl, C.1    Jäckel, P.2
  • 36
    • 75849118575 scopus 로고    scopus 로고
    • Complex logarithms in Heston-like stochastic volatility models
    • forthcoming
    • Lord, R., and Kahl, C., Complex logarithms in Heston-like stochastic volatility models. Math. Finan., 2009, forthcoming.
    • (2009) Math. Finan.
    • Lord, R.1    Kahl, C.2
  • 37
    • 53849114079 scopus 로고    scopus 로고
    • Optimal Fourier inversion in semianalytical option pricing
    • Lord, R. and Kahl, C., Optimal Fourier inversion in semianalytical option pricing. J. Comput. Finan., 2007, 10, 1-30.
    • (2007) J. Comput. Finan. , vol.10 , pp. 1-30
    • Lord, R.1    Kahl, C.2
  • 38
    • 0040519931 scopus 로고    scopus 로고
    • A simple method for generating gamma variables
    • Marsaglia, G. and Tsang, W.W., A simple method for generating gamma variables. ACM Trans. Math. Software, 2000, 26, 363-372.
    • (2000) ACM Trans. Math. Software. , vol.26 , pp. 363-372
    • Marsaglia, G.1    Tsang, W.W.2
  • 40
    • 41349119837 scopus 로고    scopus 로고
    • Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise
    • Moro, E., Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise. Phys. Rev. E, 2004, 70, 045102(R)-1-045102(R)-4.
    • (2004) Phys. Rev. E. , vol.70 , pp. 1-4
    • Moro, E.1
  • 41
    • 41949120331 scopus 로고    scopus 로고
    • Boundary preserving semi-analytic numerical algorithms for stochastic differential equations
    • Moro, E. and Schurz, H., Boundary preserving semi-analytic numerical algorithms for stochastic differential equations. SIAM J. Sci. Comput., 2007, 29, 1525-1549.
    • (2007) SIAM J. Sci. Comput. , vol.29 , pp. 1525-1549
    • Moro, E.1    Schurz, H.2
  • 44
    • 85010517306 scopus 로고    scopus 로고
    • Calculating prices and sensitivities for pathindependent derivative securities in multifactor models
    • Willard, G.A., Calculating prices and sensitivities for pathindependent derivative securities in multifactor models. J. Deriv., 1997, 5, 45-61.
    • (1997) J. Deriv. , vol.5 , pp. 45-61
    • Willard, G.A.1
  • 45
    • 0010844126 scopus 로고
    • Sur une construction des solutions d'é quations différentielles stochastiques dans le cas non-Lipschitzien, in Séminaire de Probabilité
    • (Springer: New York)
    • Yamada, T., Sur une construction des solutions d'é quations diffé rentielles stochastiques dans le cas non-Lipschitzien, in Séminaire de Probabilité, Lecture Notes in Mathematics 649 Vol. XII, pp. 114-131, 1978 (Springer: New York).
    • (1978) Lecture Notes in Mathematics , vol.649 , pp. 114-131
    • Yamada, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.