The Price of Government Bond Volatility

39 Pages Posted: 26 Apr 2013  

Antonio Mele

Swiss Finance Institute & University of Lugano; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Yoshiki Obayashi

Applied Academics LLC

Date Written: April 23, 2013


Treasury price volatility comoves with equity volatility quite heterogeneously over time, with correlations ranging from negative to positive, and marked by periods of rapid movement. What is the price of Treasury volatility? How can we express this price in a model-free format? Despite the success of the CBOE equity VIX, no counterparts exist for US Treasuries and other government bond markets. Pricing Treasury price volatility in a model-free manner is a delicate issue for two reasons. First, volatility is referenced to an asset with Â…finite maturity, a case where standard spanning arguments might fail to apply. Second, the markets we are interested in this paper obviously relate to contexts where interest rates are random, which requires tilting the basis assets we wish to price the volatility of. We develop contract designs for variance swaps applying to government bonds, and derive model-free indexes of government bond price expected volatility, based on the fair value of the contracts expressed in terms of option prices. We follow market practice and consider both percentage and basis point expected volatility. Basis point volatility can be priced in a model-free format even in the presence of jumps. We provide two algorithms to calculate the indexes through the use of American future options.

Keywords: Interest Rate Volatility, Interest Rate Variance Swaps, Model-Free Pricing, VIX Index, Basis Point Variance, Basis Point Yield Volatility, Quadratic Contracts

JEL Classification: E4, G11, G12, G13

Suggested Citation

Mele, Antonio and Obayashi, Yoshiki, The Price of Government Bond Volatility (April 23, 2013). Swiss Finance Institute Research Paper No. 13-27. Available at SSRN: or

Antonio Mele (Contact Author)

Swiss Finance Institute & University of Lugano ( email )

Via Buffi, 13
Lugano, 6900


Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Yoshiki Obayashi

Applied Academics LLC ( email )

United States

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