Volatility Indexes and Contracts for Government Bonds and Time Deposits

The volatilities of Treasury and time deposit markets comove 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 or, say, that of the Eurodollar LIBOR? How can we express these prices in a model-free format? Despite the success of the CBOE equity VIX, no counterparts exist for US Treasuries and other government bond markets, or time deposit such as the Eurodollar. Pricing Treasury volatility in a model-free manner is a delicate issue for two reasons. First, volatility is referenced to an asset with fi nite maturity, a case where standard spanning arguments might fail to apply. Second, and similarly as for time deposits, 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 time deposits, and derive model-free indexes of Treasury price and time deposits 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.