Financial density forecasts: A comprehensive comparison of risk‐neutral and historical schemes

Abstract

We investigate the forecasting ability of the most commonly used benchmarks in financial economics. We approach the usual caveats of probabilistic forecasts studies-small samples, limited models, and nonholistic validations-by performing a comprehensive comparison of 15 predictive schemes during a time period of over 21 years. All densities are evaluated in terms of their statistical consistency, local accuracy and forecasting errors. Using a new composite indicator, the integrated forecast score, we show that risk-neutral densities outperform historical-based predictions in terms of information content. We find that the variance gamma model generates the highest out-of-sample likelihood of observed prices and the lowest predictive errors, whereas the GARCH-based GJR-FHS delivers the most consistent forecasts across the entire density range. In contrast, lognormal densities, the Heston model, or the nonparametric Breeden-Litzenberger formula yield biased predictions and are rejected in statistical tests.

The recovery theorem with application to risk management

“…t , S 0 the spot rate, and V 0 the spot variance. It is well-known that adding jumps to the spot price process could improve the agreement between theoretical and observed option prices, especially in stressed markets (see e.g., Crisóstomo and Couso, 2018). Therefore, the Bates model is simply an extension of the Heston model with independent jumps added to the security price dynamics in (2.7), giving the following risk-neutral dynamics:…”

“…The ability to accurately forecast future asset prices is an important and frequently studied problem in financial economics (see e.g., Bollerslev et al, 2009;Crisóstomo and Couso, 2018). The recent global financial crisis highlighted this problem, where many conventional financial theories were unable to realistically forecast risk measures.…”

“…In particular, historical simulation and risk-neutral methods are the most widely used methods in financial risk management, where most financial institutions prefer to use historical simulations to manage risk (see Pérignon and Smith, 2010). However, Christoffersen et al (2013) and Crisóstomo and Couso (2018) found that methods based on option-implied information generally outperformed historical-based estimates. Similarly, Shackleton et al (2010) compared the real-world option-implied densities to that of historical densities, where they found that the real-world option-implied forecasts for two-and four-week horizons were superior to that of the historical forecasts.…”

Distribution Prediction of Decomposed Relative EVA Measure with Levy-Driven Mean-Reversion Processes: The Case of an Automotive Sector of a Small Open Economy

“…Other researchers further analysed and developed this problem, e.g., [28,[40][41][42][43][44][45][46]. Several authors [1,[47][48][49][50][51][52] dealt with probability distribution forecasting for predicting uncertainty. (d) The procedures and advantages of disaggregated (multifactor) forecasting are described in [53][54][55].…”

“…The first one is based on the probability integral transform of the distribution and a comparison with the uniform distribution. The closer the uniform distribution, the better the forecasting distribution is (see [49,52,60,61]). The scoring method investigates the relative evaluation of two distributions, and a higher score means a better forecast distribution [47,[62][63][64][65].…”