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Is the choice between a log-normal and a mean-reverting process for the underlying asset important?

April 26, 2017ASSET log-normal process underlying

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Is the choice between a log-normal and a mean-reverting process for the underlying asset important?

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Professor Robert Merton of HBS, and the 1997 Nobel Prize winner in Economics, has the following test question in his MBA Finance class: Suppose you have two option contracts with the same terms. The first contract is on “soap” (or some product) and the underlying asset is a future contract on soap. Soap is known to have a geometric brownian motion (GBM) process. The second contract is on “butter” and the underlying asset is a futures contract on butter. Butter has a mean-reverting process. Sigma is the same for the two futures contracts. Which option is more valuable?