  In this paper we study dynamic pricing mechanisms of financial derivatives. A
typical model of such pricing mechanism is the so-called g--expectation defined
by solutions of a backward stochastic differential equation with g as its
generating function. Black-Scholes pricing model is a special linear case of
this pricing mechanism. We are mainly concerned with two types of pricing
mechanisms in an option market: the market pricing mechanism through which the
market prices of options are produced, and the ask-bid pricing mechanism
operated through the system of market makers. The later one is a typical
nonlinear pricing mechanism. Data of prices produced by these two pricing
mechanisms are usually quoted in an option market.
  We introduce a criteria, i.e., the domination condition (A5) in (2.5) to test
if a dynamic pricing mechanism under investigation is a g--pricing mechanism.
This domination condition was statistically tested using CME data documents.
The result of test is significantly positive. We also provide some useful
characterizations of a pricing mechanism by its generating function.
