General Theory of Geometric Lévy Models for Dynamic Asset Pricing

Details General Theory of Geometric Lévy Models for Dynamic Asset Pricing General Theory of Geometric Lévy Models for Dynamic Asset Pricing

2011-11-09

arxiv.org/abs/1111.2169v2

Economy

Quantitative Finance

Pricing of Securities

20 pages, version to appear in Proceedings of the Royal Society London A

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

General Theory of Geometric Lévy Models for Dynamic Asset Pricing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with General Theory of Geometric Lévy Models for Dynamic Asset Pricing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Theory of Geometric Lévy Models for Dynamic Asset Pricing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-42494