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Negative Probabilities in Financial Modeling

24 Pages Posted: 1 Mar 2011  

Gunter A. Meissner

University of Hawaii - Shidler College of Business

Dr. Mark Burgin

University of California, Los Angeles (UCLA) - Department of Mathematics

Date Written: February 28, 2011

Abstract

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.

Keywords: Negative Probabilities, Negative Interest Rates, Caps, Floors

JEL Classification: C10

Suggested Citation

Meissner, Gunter A. and Burgin, Dr. Mark, Negative Probabilities in Financial Modeling (February 28, 2011). Available at SSRN: https://ssrn.com/abstract=1773077 or http://dx.doi.org/10.2139/ssrn.1773077

Gunter A. Meissner (Contact Author)

University of Hawaii - Shidler College of Business ( email )

2404 Maile Way
Honolulu, HI 96822
United States

Dr. Mark Burgin

University of California, Los Angeles (UCLA) - Department of Mathematics ( email )

Los Angeles, CA 90095-1481
United States

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