Volatility Indices and Implied Uncertainty Measures of European Government Bond Futures

Abstract

Implied volatility and other forward-looking measures of option-implied uncertainty help investors carefully evaluate market sentiment and expectations. We construct several measures of implied uncertainty in European government bond futures. In the first part, we create new volatility indices, which reflect market pricing of subsequently realised volatility of underlying bond futures. We express volatility indices in both price and basis points, the latter being more intuitive to interpret; we document their empirical properties, and discuss their possible applications. In the second part, we fit the volatility smile using the SABR model, and recover option-implied probability distribution of possible outcomes of bond futures prices. We analyse shapes of the implied distribution, track its quantiles over time, calculate its skewness and kurtosis, and infer probabilities of a given upside or downside move in the price of bond futures or in the yield of their underlying CTD bond. We illustrate these complementary measures throughout the note using Bund futures as an example, and show the results for Schatz, Bobl, OAT, and BTP futures in the annex. Such forward-looking measures help market participants quantify the degree of future market uncertainty and thoroughly assess what risks are priced in.

Keywords: bond futures, market expectations, options, probability density function, SABR, VIX, volatility index

JEL Classification: C13, G13, G14, G17