The theory of L\'evy models for asset pricing simplifies considerably if one
takes a pricing kernel approach, which enables one to bypass market
incompleteness issues. The special case of a geometric L\'evy model (GLM) with
constant parameters can be regarded as a natural generalisation of the standard
geometric Brownian motion model used in the Black-Scholes theory. In one
dimension, once the underlying L\'evy process has been specified, the GLM is
characterised by four parameters: the initial asset price, the interest rate,
the volatility, and a risk aversion factor.