Kullback-Liebler Information criterion for density forecasts evaluation: New empirical evidence for stock index returns
Abstract: This paper introduces a novel approach to calibration transformation, aiming at transforming option-implied risk-neutral density into real-world density forecasts using options contracts and historical index prices. As a result, the latter accounts for investors’ subjective attitude to risks. We provide new evidence on the forecasting abilities of option-implied information by extracting and evaluating density forecasts of stock index returns. We use the Kullback-Liebler information criterion (KLIC) to measure the distance between the true-unknown density and empirical densities derived over multiple horizons. This paper suggests that historical density forecasts provide better results than option-implied risk-neutral and real-world calibrated density forecasts.
Keywords: Density; Forecasts; Implied-information; KLIC; Calibration-transformation; JEL: C58, G12, G13, G 17
Presented earlier versions at:
April 2025: IFABS Oxford
September 2022: IFABS Naples (University of Naples Frederico II)
March 2022: Economics Finance and Accounting internal seminar (University of Leicester)
July 2023 30th Finance Forum Spain Malaga