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Perturbative Approach on Financial Markets

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  • Simone Scotti

Abstract

We study the point of transition between complete and incomplete financial models thanks to Dirichlet Forms methods. We apply recent techniques, developped by Bouleau, to hedging procedures in order to perturbate parameters and stochastic processes, in the case of a volatility parameter fixed but uncertain for traders; we call this model Perturbed Black Scholes (PBS) Model. We show that this model can reproduce at the same time a smile effect and a bid-ask spread; we exhibit the volatility function associated to the local-volatility model equivalent to PBS model when vanilla options are concerned. Lastly, we present a connection between Error Theory using Dirichlet Forms and Utility Function Theory.

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  • Simone Scotti, 2008. "Perturbative Approach on Financial Markets," Papers 0806.0287, arXiv.org.
    • Handle: RePEc:arx:papers:0806.0287
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    References listed on IDEAS

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    1. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
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    1. Simone Scotti, 2010. "The impact of uncertainties on the pricing of contingent claims," Papers 1001.5202, arXiv.org.

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