Time Consistent Bid-Ask Dynamic Pricing Mechanisms for Contingent Claims and Its Numerical Simulations Under Uncertainty
AbstractWe study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng (). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the drift uncertainty and volatility uncertainty of the stock price process. Using the techniques on G-framework we show that the risk premium of the asset is uncertain and distributed with maximum distribution. A time consistent G-expectation is defined by the viscosity solution of the G-heat equation. Using the time consistent G-expectation we define the G dynamic pricing mechanism for the claim. We prove that G dynamic pricing mechanism is the bid-ask Markovian dynamic pricing mechanism. The full nonlinear PDE is derived to describe the bid (resp. ask) price process of the claim. Monotone implicit characteristic finite difference schemes for the nonlinear PDE are given, nonlinear iterative schemes are constructed, and the simulations of the bid (resp. ask) prices of contingent claims under uncertainty are implemented.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1111.4298.
Date of creation: Nov 2011
Date of revision: Sep 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-28 (All new papers)
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- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor and Francis Journals, vol. 2(2), pages 73-88.
- Wei Chen, 2013. "Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty," Papers 1306.4070, arXiv.org.
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