Negative Probabilities in Financial Modeling
Gunter A. Meissner
University of Hawaii - Shidler College of Business
Dr. Mark Burgin
University of California, Los Angeles (UCLA) - Department of Mathematics
February 28, 2011
We first define and derive general properties of negative probabilities. We then show how negative probabilities can be applied to modeling financial options such as Caps and Floors. In trading practice, these options are typically valued in a Black-Scholes-Merton framework assuming a lognormal distribution for the underlying interest rate. However, in some cases, such as the 2008/2009 financial crisis, interest rates can get negative. Then the lognormal distribution is inapplicable. We show how negative probabilities associated with negative interest rates can be applied to value interest rate options. A model in VBA, which prices Caps and Floors with negative probabilities, is available upon request. A follow up paper will address bigger than unity probabilities in financial modeling.
Number of Pages in PDF File: 24
Keywords: Negative Probabilities, Negative Interest Rates, Caps, Floors
JEL Classification: C10
Date posted: March 1, 2011
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