Find in Library

We analyze the predictability of daily data on the CBOE <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>I</mi><mi>X</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>K</mi><mi>E</mi><mi>W</mi></mrow></semantics></math></inline-formula> indices, used to capture the average level of risk-neutral risk and downside risk, respectively, as implied by S&P 500 index options. In particular, we use forecast models from the Heterogeneous Autoregressive (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>A</mi><mi>R</mi></mrow></semantics></math></inline-formula>) class to test whether and how lagged values of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>I</mi><mi>X</mi></mrow></semantics></math></inline-formula> and of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>K</mi><mi>E</mi><mi>W</mi></mrow></semantics></math></inline-formula> may increase the forecasting power of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>A</mi><mi>R</mi></mrow></semantics></math></inline-formula> for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>K</mi><mi>E</mi><mi>W</mi></mrow></semantics></math></inline-formula> and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>I</mi><mi>X</mi></mrow></semantics></math></inline-formula>. We find that a simple <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>A</mi><mi>R</mi></mrow></semantics></math></inline-formula> is very hard to beat in out-of-sample experiments aimed at forecasting the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>I</mi><mi>X</mi></mrow></semantics></math></inline-formula>. In the case of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>K</mi><mi>E</mi><mi>W</mi></mrow></semantics></math></inline-formula>, the benchmarks (the random walk and an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>) are clearly outperformed by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>A</mi><mi>R</mi></mrow></semantics></math></inline-formula> models at all the forecast horizons considered and there is evidence that special definitions of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>K</mi><mi>E</mi><mi>W</mi></mrow></semantics></math></inline-formula> index based on put options data only yield superior forecasts at all horizons.