The Price of Government Bond Volatility

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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 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.