IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1111.2169.html
   My bibliography  Save this paper

General Theory of Geometric L\'evy Models for Dynamic Asset Pricing

Author

Listed:
  • Dorje C. Brody
  • Lane P. Hughston
  • Ewan Mackie

Abstract

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.

Suggested Citation

  • Dorje C. Brody & Lane P. Hughston & Ewan Mackie, 2011. "General Theory of Geometric L\'evy Models for Dynamic Asset Pricing," Papers 1111.2169, arXiv.org, revised Jan 2012.
  • Handle: RePEc:arx:papers:1111.2169
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1111.2169
    File Function: Latest version
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500042 is not listed on IDEAS
    2. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    3. Islyaev, Suren & Date, Paresh, 2015. "Electricity futures price models: Calibration and forecasting," European Journal of Operational Research, Elsevier, vol. 247(1), pages 144-154.
    4. Watson, John G. & Scott, Jason S., 2014. "Ratchet consumption over finite and infinite planning horizons," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 84-96.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1111.2169. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.