A Behavioral Explanation for the Negative Asymmetric Return-Volatility Relation

The Intraday and Overnight Behavior of SPY Options and Adjusted Delta Hedging

“…Overall, the negative response of implied volatility to positive and negative SPY returns is symmetric over intraday intervals but asymmetric over overnight intervals where implied volatility responds more sluggishly to positive than to negative SPY returns. Thus, the overnight but not the intraday results are consistent with Low (2004), Giot (2005), Hibbert et al (2008), and Ederington and Guan (2010), who find that the VIX over daily intervals rises more in response to S&P 500 index declines than it falls in response to S&P 500 index increases. However, unreported results indicate that when the intraday and overnight intervals are aggregated into daily intervals, the results are consistent with these previous studies.…”

“…Thus, positive and negative SPY returns have equal-magnitude effects on implied volatility, consistent with evidence presented earlier that the direction more so than the magnitude of SPY returns drives implied volatility. This finding also indicates that the empirical regularity documented by Low (2004), Giot (2005), Hibbert et al (2008), and Ederington and Guan (2010) that the VIX rises considerably more in response to negative S&P index returns than it falls in response to equal-magnitude positive returns is not present in SPY options over intraday intervals.…”

“…For the sake of brevity, this note focuses on the tests of whether the variance of the P&L with empirically adjusted (EMP) deltas is less in percentage terms than with BSM deltas. those of Low (2004), Giot (2005), Hibbert et al (2008), and Ederington and Guan (2010), who find that over daily intervals the VIX rises more in response to stock price declines than the VIX falls in response to stock price increases. However, the overnight results are consistent with these earlier studies in that implied volatility is far more responsive to SPY price declines than increases and much of the inverse relationship between overnight implied volatility changes and SPY returns owes to negative SPY price changes.…”

“…By contrast, research focusing on the relationship between implied volatility changes and equity returns, such as Giot (2005), Low (2004), Hibbert, Daigler, & Dupoyet (2008), and Ederington and Guan (2010), demonstrate that implied volatility as captured by the CBOE Volatility Index (VIX) moves in the opposite direction of equity prices and falls in the face of large positive equity returns. Low (2004) and Hibbert et al (2008) interpret this phenomenon in a behavioral light as reflecting fear growing faster than complacency. Ederington and Guan (2010) also demonstrate that the finding that the VIX falls in response to positive equity returns is consistent with a tendency of realized volatility constructed from intraday equity returns to decrease following positive equity returns.…”

A Term Structure Model for VIX Futures

“…10 Two theories explaining the negative return-volatility relation are the leverage effect hypothesis (Black, 1976a) and the volatility feedback hypothesis (Campbell and Hentschel, 1992;Poterba and Summers, 1986). Hibbert, Daigler, and Dupoyet (2008) explain this relation using behavioral concepts. Kernel estimate of the VIX futures returns and the normal and NIG distributions.…”