Forecasting volatility under fractality, regime-switching, long memory and student- innovations

2010 ◽  
Vol 54 (11) ◽  
pp. 2676-2692 ◽  
Author(s):  
Thomas Lux ◽  
Leonardo Morales-Arias
Keyword(s):  
Long Memory ◽  
Regime Switching ◽  
Forecasting Volatility

Random coefficient autoregression, regime switching and long memory

2003 ◽  
Vol 35 (03) ◽  
pp. 737-754 ◽  
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Renewal Process ◽  
Long Memory ◽  
Regime Switching ◽  
Covariance Function ◽  
Random Coefficient ◽  
Levy Process ◽  
Partial Sums ◽  
Stable Lévy Process

We discuss long-memory properties and the partial sums process of the AR(1) process {X t , t ∈ 𝕫} with random coefficient {a t , t ∈ 𝕫} taking independent values A j ∈ [0,1] on consecutive intervals of a stationary renewal process with a power-law interrenewal distribution. In the case when the distribution of generic A j has either an atom at the point a=1 or a beta-type probability density in a neighborhood of a=1, we show that the covariance function of {X t } decays hyperbolically with exponent between 0 and 1, and that a suitably normalized partial sums process of {X t } weakly converges to a stable Lévy process.

Forecasting Volatility Using Long Memory and Comovements: An Application to Option Valuation under SFAS 123R

2010 ◽  
Vol 45 (2) ◽  
pp. 503-533 ◽  
Author(s):  
George J. Jiang ◽  
Yisong S. Tian
Keyword(s):  
Long Memory ◽  
Financial Accounting ◽  
Option Valuation ◽  
Volatility Model ◽  
Forecasting Performance ◽  
Market Factors ◽  
Performance Forecasting ◽  
Long Term Forecasting ◽  
Forecasting Volatility

AbstractHorizon-matched historical volatility is commonly used to forecast future volatility for option valuation under the Statement of Financial Accounting Standards (SFAS) 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. In 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 that shrinkage adjustment toward 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.

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