Modelling Derivatives Pricing Mechanisms with Their Generating Functions

TL;DR

This paper explores dynamic derivatives pricing mechanisms using generating functions, comparing market and ask-bid models, and introduces a statistical test for identifying g-pricing mechanisms with positive results on CME data.

Contribution

It introduces a domination condition to identify g-pricing mechanisms and provides characterizations of pricing models based on their generating functions.

Findings

The domination condition effectively tests for g-pricing mechanisms.

Market data supports the positive application of the domination condition.

Characterizations help distinguish different types of pricing mechanisms.

Abstract

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.