Forecasting Volatility Using Long Memory and Comovements: An Application to Option Valuation Under SFAS 123r

Abstract

Horizon-matched historical volatility is commonly used to forecast future volatility for option valuation under the Statement of Financial Accounting Standards 123R. In this paper, we empirically investigate the performance of using historical volatility to forecast long-term stock return volatility in comparison with a number of alternative forecasting methods. Analyzing forecasting errors and their impact on reported income due to option expensing, we find that historical volatility is a poor forecast for long-term volatility and shrinkage adjustment towards comparable-firm volatility only slightly improves its performance. Forecasting performance can be improved substantially by incorporating both long memory and comovements with common market factors. We also experiment with a simple mixed-horizon realized volatility model and find its long-term forecasting performance to be more accurate than historical forecasts but less accurate than long-memory forecasts.

Keywords: Volatility forecasting, Option expensing, Historical volatility, Shrinkage forecast, Long memory, Fractional integration, Comovements

JEL Classification: G13, G18, G38, M52, E37