Recovery with Applications to Forecasting Equity Disaster Probability and Testing the Spanning Hypothesis in the Treasury Market

Gurdip S. Bakshi, Xiaohui Gao, and Jinming Xue

We investigate the implications of recovering real-world conditional expectation of return functions using options on the S&P 500 index and Treasury bond futures. First, we construct estimates of the probability of disasters, defined as higher than 6%, 5%, or 4% equity market declines over option expiration cycles. This measure of disaster probability forecasts realized disasters. Second, we employ options on the futures of the 10- and 30-year Treasury bonds to construct estimates for the expected return of bond futures. These measures display forecasting ability for subsequent futures returns beyond the level, slope, and curvature variables extracted from the yield curve.