Parametric Bootstrap Tests for Futures Price and Implied Volatility Biases with Application to Rating Livestock Margin Insurance for Dairy Cattle
A common approach in the literature, whether the investigation is about futures price risk premiums or biases in option-based implied volatility coefficients, is to use samples in which consecutive observations can be regarded as uncorrelated. That will be the case for non- overlapping forecast horizons constructed by either focusing on short time-to-maturity contracts or excluding some data. In this article we propose a parametric bootstrap procedure for uncovering futures and options biases in data characterized by overlapping horizons and correlated prediction errors. We apply our method to test hypotheses that futures prices are efficient and unbiased predictors of terminal prices, and that squared implied volatility, multiplied by time left to option expiry, is an unbiased predictor of terminal log-price variance. We apply the test to corn, soybean meal and Class III milk futures and options data for the period 2000-2011. We find evidence for downward bias in soybean meal futures, as well as downward volatility bias in Class III milk options. Importance of these results is illustrated on the example of premium determination for Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy).
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