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  Far East Journal of Theoretical Statistics  
 ISSN: 0972-0863
 
 
 

     Far East Journal of Theoretical Statistics
    Volume 30, Issue 1, Pages 1 - 39 (January 2010)


ASYMPTOTICS FOR OPTION PRICING IN STOCHASTIC VOLATILITY ENVIRONMENT

K. Narita

Received August 6, 2009

References:



[1] K. Andersson, Stochastic volatility, Project Report 2003:18, Dept. of Math., Uppsala Univ., 2003, pp. 1-34.

[2] F. Biagini, Y. Hu, B. Øksendal and A. Sulem, A stochastic maximum principle for processes driven by fractional Brownian motion, Stoch. Proc. Appl. 100(1-2) (2002), 233-253.

[3] F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer-Verlag, London Ltd., 2008.

[4] F. Comte and E. Renault, Long memory in continuous-time stochastic volatility models, Math. Finance 8(4) (1998), 291-323.

[5] P. Cotton, J.-P. Fouque, G. Papanicolaou and R. Sircar, Stochastic volatility corrections for interest rate derivatives, Math. Finance 14(2) (2004), 173-200.

[6] T. E. Duncan, Y. Hu and B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion, I, Theory, SIAM J. Control Optim. 38(2) (2000), 582-612.

[7] J.-P. Fouque, G. Papanicolaou and K. R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge Univ. Press, Cambridge, UK, 2000.

[8] J.-P. Fouque, G. Papanicolaou, R. Sircar and K. Solna, Singular perturbations in option pricing, SIAM J. Appl. Math. 63(5) (2003), 1648-1665.

[9] G. Gripenberg and I. Norros, On the prediction of fractional Brownian motion, J. Appl. Probab. 33(2) (1996), 400-410.

[10] H. Holden, B. Øksendal, J. Ubøe and T. Zhang, Stochastic Partial Differential Equations, A Modeling, White Noise Functional Approach, Birkhäuser Boston, Inc., Boston, 1996.

[11] Y. Hu, Option pricing in a market where the volatility is driven by fractional Brownian motions, Recent Developments in Mathematical Finance (Shanghai, 2001), pp. 49-59, World Sci. Publ., River Edge, NJ, 2002.

[12] Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc. 175(825) (2005), viii + 127pp.

[13] Y. Hu and B. Øksendal, Fractional white noise calculus and applications to finance, Infinite Dim. Anal. Quantum Probab. Relat. Top. 6(1) (2003), 1-32.

[14] M. Jonsson and K. R. Sircar, Partial hedging in a stochastic volatility environment, Math. Finance 12(4) (2002), 375-409.

[15] G. Kallianpur and R. L. Karandikar, Introduction to Option Pricing Theory, Birkhäuser, Boston, 2000.

[16] Y. S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Springer-Verlag, Berlin, Heidelberg, 2008.

[17] K. Narita, Nonexplosion criteria for solutions of SDE with fractional Brownian motion, Stoch. Anal. Appl. 25(1) (2007), 73-88.

[18] K. Narita, Pathwise uniqueness of solutions of SDE in a fractional Brownian environment, Far East J. Math. Sci. (FJMS) 27(1) (2007), 121-146.

[19] K. Narita, Stochastic analysis of fractional Brownian motion and application to Black-Scholes market, Far East J. Math. Sci. (FJMS) 30(1) (2008), 65-135.

[20] C. Necula, Option pricing in a fractional Brownian motion environment, Draft, Academy of Economic Studies, Bucharest, Romania, February 12, 2002, pp. 1-18.

[21] D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Springer-Verlag, Berlin, Heidelberg, 2006.

Keywords and phrases: fractional Brownian motion, Ornstein-Uhlenbeck process, fractional Ito-integral, stochastic differential equation, Black-Scholes equation, European call option.

 


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