Abstract
We study in this paper an extension of the Black Scholes approach to take account of frictions in financial markets. The frictions we consider are related to costs linked to holding a portfolio of securities. The friction model is relatively general, the only limitation being that the friction affects the wealth function continuously, and not impulsively, as it is the case when modelling transaction costs. So our model differs from Davis, Panas and Zariphopoulou (1993), but ideas concerning the definition of selling and buying prices of options are taken from their approach. We shall consider European as well as Americans options. Interesting differences will be apparent.
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References
Bensoussan A. and Lions J.L. (1978) Applications of Variational Inequalities in Stochastic Control, North Holland.
Davis, M.H.A., Panas, V.G., Zariphopoulou (1993) European option pricing with transaction costs, SIAM J. Control Optim.
Fleming W.H, Rishel R.W. (1975) Deterministic and Stochastic Optimal Control, Springer-Verlag.
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© 1999 Springer Science+Business Media New York
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Bensoussan, A., Julien, H. (1999). Option Pricing in a Market with Frictions. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_31
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_31
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
Online ISBN: 978-1-4612-1784-8
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