Determination of the probability distribution measures from market option prices using the method of maximum entropy in mean Articles uri icon

publication date

  • June 2012

start page

  • 299

end page

  • 312

issue

  • 4

volume

  • 19

International Standard Serial Number (ISSN)

  • 1350-486X

abstract

  • We consider the problem of recovering the risk-neutral probability distribution of the price of an asset, when the information available consists of the market price of derivatives of European type having the asset as underlying. The information available may or may not include the spot value of the asset as data. When we only know the true empirical law of the underlying, our method will provide a measure that is absolutely continuous with respect to the empirical law, thus making our procedure model independent. If we assume that the prices of the derivatives include risk premia and/or transaction prices, using this method it is possible to estimate those values, as well as the no-arbitrage prices. This is of interest not only when the market is not complete, but also if for some reason we do not have information about the model for the price of the underlying.