  The geometric L\'evy model (GLM) is a natural generalisation of the geometric
Brownian motion model (GBM) used in the derivation of the Black-Scholes
formula. The theory of such models simplifies considerably if one takes a
pricing kernel approach. In one dimension, once the underlying L\'evy process
has been specified, the GLM has four parameters: the initial price, the
interest rate, the volatility, and the risk aversion. The pricing kernel is the
product of a discount factor and a risk aversion martingale. For GBM, the risk
aversion parameter is the market price of risk. For a GLM, this interpretation
is not valid: the excess rate of return is a nonlinear function of the
volatility and the risk aversion. It is shown that for positive volatility and
risk aversion the excess rate of return above the interest rate is positive,
and is increasing with respect to these variables. In the case of foreign
exchange, Siegel's paradox implies that one can construct foreign exchange
models for which the excess rate of return is positive both for the exchange
rate and the inverse exchange rate. This condition is shown to hold for any
geometric L\'evy model for foreign exchange in which volatility exceeds risk
aversion.
