The Pricing Mechanism of Contingent Claims and its Generating Function

In this paper we study dynamic pricing mechanism of contingent claims. A typical model of such pricing mechanism is the so-called g-expectation $E_{s,t}^g[X]$ defined by the solution of the backward stochastic differential equation with generator g and with the contingent claim X as terminal condition. The generating function g this BSDE. We also provide examples of determining the price generating function $g=g(y,z)$ by testing. The main result of this paper is as follows: if a given dynamic pricing mechanism is $E^{g_{\mu }}$-dominated, i.e., the criteria (A5) $E_{s,t}[X]-E_{s,t}[X^{\mathrm{\prime }}]\le E_{s,t}^{g_{\mu }}[X-X^{\mathrm{\prime }}]$ is satisfied for a large enough $\mu >0$, where $g_{\mu }=g_{\mu }(\mathrm{\mid }y\mathrm{\mid }+\mathrm{\mid }z\mathrm{\mid })$, then $E_{s,t}$ is a g-pricing mechanism. This domination condition was statistically tested using CME data documents. The result of test is significantly positive.