IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

The Empirical Performance of Option Based Densities of Foreign Exchange

  • Keller, Joachim G.
  • Craig, Ben R.

Risk neutral densities (RND) can be used to forecast the price of the underlying basis for the option, or it may be used to price other derivates based on the same sequence. The method adopted in this paper to calculate the RND is to firts estimate daily the diffusion process of the underlying futures contract for foreign exchange, based on the price of the American puts and calls reported on the Chicago Mercentile Exchange for the end of the day. This process implies a risk neutral density for each point of time in the future on each day. I order to estimate the diffusion process we need methods of calculating the prices of American options that are fast and accurate. The numercial problems posed by American options are tough. We solve the pricing of American options by using higher order lattices combined with smoothing the value function of the American Option at the boundaries in order to mitigate the non-differentiability of both the payoff boundary at expiration and the early exercise boundary. By calculating the price of an American option quickly, we can estimate the diffusion process by minimizing the squared distance between the calculated prices and the observed prices in the data. This paper also tests wheter the densities provided from American options provide a good forecasting tool. We use a non-parametric test of the densities that depends on inverse probabilities. A problem with the use of these tests in the past has been the time series nature of the transformed variables when the forecasting windows overlap. The inverse probability of the realized thirty day ahead spot at time t is correlated with the corresponding inverse probability at time t-1, because the development of the spot rate untill t shares twenty-nine days of history. We modify the tests based on the inverse probability function to account for this correlation between our random variables that are uniform distributed under the null hypothesis. We find that the densities based on the American option prices for foreign exchange do considerably well for the thirty to sixty day time horizon, but less well for the shorter horizons. The most sophisticated single state model of the diggusion process did best at the one-hundred-eighty day horizon.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2002,07.

in new window

Date of creation: 2002
Date of revision:
Handle: RePEc:zbw:bubdp1:4172
Contact details of provider: Postal: Postfach 10 06 02, 60006 Frankfurt
Phone: 0 69 / 95 66 - 34 55
Fax: 0 69 / 95 66 30 77
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:zbw:bubdp1:4172. 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: (ZBW - German National Library of Economics)

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.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.