The recovery theorem with application to risk management

Abstract

The forward-looking nature of option prices provides an appealing way to extract risk measures. In this paper, we extract forecast densities from option prices that can be used in forecasting risk measures. More specifically, we extract a real-world return density forecast, implied from option prices, using the recovery theorem. In addition, we backtest and compare the predictive power of this real-world return density forecast with a risk-neutral return density forecast, implied from option prices, and a simple historical simulation approach. In an empirical study, using the South African FTSE/JSE Top 40 index, we found that the extracted real-world density forecasts, using the recovery theorem, yield satisfying forecasts of risk measures.