The optimal hedging price of a European type contingent claim
Author:
S. V. Posashkov
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 77 (2008), 147-154
MSC (2000):
Primary 60H30; Secondary 60J35, 60J65
DOI:
https://doi.org/10.1090/S0094-9000-09-00753-4
Published electronically:
January 21, 2009
MathSciNet review:
2432778
Full-text PDF Free Access
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Abstract: A $(B,S)$ financial market is considered in the paper for the case where the volatility is governed by fractional Brownian motion. We prove that the market is incomplete and find the optimal hedging price of a contingent claim that locally minimizes the risk. Under certain assumptions on the price function, we obtain a partial differential equation for the fair hedging price of a contingent claim.
References
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- Gopinath Kallianpur and Rajeeva L. Karandikar, Introduction to option pricing theory, Birkhäuser Boston, Inc., Boston, MA, 2000. MR 1718056
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References
- I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion, Bernoulli 5(4) (1999), 571–587. MR 1704556 (2000f:60053)
- G. Kallianpur and R. L. Karandinkar, Introduction to Option Pricing Theory, Birkhäuser, Boston, 2000. MR 1718056 (2000k:91054)
- S. V. Posashkov, Studies of the ($B,S$) market of assets with a stochastic volatility governed by a fractional Brownian motion, Visnyk Kyiv University 2 (2005), 56–61. (Ukrainian)
- P. Cheridito, Regularizing Fractional Brownian Motion with a View towards Stock Price Modeling, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich, 2001.
- M. Hitsuda, Representation of Gaussian processes equivalent to Wiener process, Osaka J. Math. 5 (1968), 299–312. MR 0243614 (39:4935)
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- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1991. MR 1121940 (92h:60127)
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Additional Information
S. V. Posashkov
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
corlagon@univ.kiev.ua
Keywords:
Optimal hedging price,
fractional Brownian motion,
European type contingent claim
Received by editor(s):
August 31, 2006
Published electronically:
January 21, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
