The Volatility of Low Rates

11 Pages Posted: 20 Jul 2020

See all articles by Raphael Douady

Raphael Douady

CES Univ. Paris 1; Riskdata; Stony Brook university

Date Written: November 5, 2013


Traditional, fixed-income risk models are based on the assumption that bond risk is directly proportional to the interest rate, i.e. that the interest-rate distribution is "log-normal." Two corollaries would then follow. Firstly, nominal interest rates could never be negative. Furthermore, bond volatility vanishes when interest rates approach zero. These conclusions are obviously wrong, if we observe the debt situation in a country such as Germany. Should we then infer that the traditional way to model fixed income is no longer valid? Our study, based on bond-data back tests, covering 40 years that encompass both periods of low rates and of high inflation, demonstrates that the traditional approach still applies. When interest rates are low, the bond risk is proportional to the rate, increased by 1%. As an example, when interest rates shift from 1% to 0%, the bond risk is divided by 2, instead of becoming null. The second conclusion is that the interest rate volatility behaves as if the absolute minimum level for a rate was not zero, but -1%.

Keywords: Interest rate models, fixed income volatility, LIBOR, fixed income option pricing, financial risk

JEL Classification: G10, G12

Suggested Citation

Douady, Raphael, The Volatility of Low Rates (November 5, 2013). Available at SSRN: or

Raphael Douady (Contact Author)

CES Univ. Paris 1 ( email )

106 bv de l'Hôpital
Paris, 75013

Riskdata ( email )

6, rue de l'Amiral Coligny
Paris, 75001


Stony Brook university ( email )

Stony Brook, NY NY 10017
United States
9174769417 (Phone)
10017-2146 (Fax)

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