Interest Rate Volatility: A Consol Rate Approach

Vincent Brousseau¹, Alain Durré²

¹Visiting Scholar at Lille 2-Skema Management Research Center-Centre National de la Recherche Scientifique (E.A. 4112), Lille, France.
²IéSEG-School of Management (Lille Catholic University) and LEM-Centre National de la Recherche Scientifique (U.M.R. 8179), Paris, France.

DOI: 10.4236/jmf.2015.51006                

Abstract

In this paper, we propose a new methodology to estimate the volatility of interest rates in the euro area money market. In particular, our approach aims at avoiding the limitations of market implied volatilities, i.e. the dependency on arbitrary choices in terms of maturity and frequencies and/or of other factors like credit and liquidity risks. The measure is constructed as the implied instantaneous volatility of a consol bond that would be priced on the EONIA swap curve over the sample period from 4 January 1999 to 21 November 2013. Our findings show that this measure tracks well the historical volatility since, by dividing the consol excess returns by our volatility measure. This removes nearly entirely excess of kurtosis and volatility clustering, bringing the excess returns close to an ordinary Gaussian white noise.

Keywords

Consol Rate, Historical Volatility, Overnight Money Market, Interbank Offered Interest Rates

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Brousseau, V. and Durré, A. (2013) Interest Rate Volatility: A consol Rate-Based Measure. ECB Working Paper Series 1505.
[2]	Fisher, L. and Weil, R.L. (1971) Coping with the Risk of Interest-Rate. Journal of Business, 44, 408-431. http://dx.doi.org/10.1086/295402
[3]	Heath, D., Jarrow, R. and Morton, A. (1992) Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica, 60, 77-105. http://dx.doi.org/10.2307/2951677
[4]	Duffie, D. and Kan, R. (1996) A Yield factor Model of Interest Rates. Mathematical Finance, 6, 379-406. http://dx.doi.org/10.1111/j.1467-9965.1996.tb00123.x
[5]	Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188. http://dx.doi.org/10.1016/0304-405X(77)90016-2
[6]	Cox, J., Ingersoll, J. and Ross, S. (1979) Duration and the Measurement of Basis Risk. Journal of Business, 52, 51-61. http://dx.doi.org/10.1086/296033
[7]	Brousseau, V. (2002) The Functional Form of Yield Curves. ECB Working Paper Series 148.
[8]	Gourieroux, C. and Sufana, R. (2006) A Classification of Two-Fact or Affine Diffusion Term Structure Models. Journal of Financial Econometrics, 4, 31-52. http://dx.doi.org/10.1093/jjfinec/nbj003
[9]	Brousseau, V. and Durré, A. (2014) Sur une représentation paramétrique affine de la courbe des taux. Revue Bancaire et Financière, 4, 297-310.