Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2011-11-18
Economy
Quantitative Finance
Pricing of Securities
Scientific paper
We study dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng (2005). We consider a financial market consists 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. 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 dynamic of the claims. Monotone characteristic finite difference schemes for the nonlinear PDE are given, and the simulations of the bid (resp. ask) prices of contingent claims with uncertainty are implemented.
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