Volatility Index and Price Discovery:A General Model Inspired by China Market
This paper presents an approximate upper bound for the equity premium,utilizing a generalized volatility index named LVIX.LVIX is derived from index option prices and is designed to account for potential deviations from put-call parity.The motivation for constructing LVIX emerges from the observation that both the VIX and SVIX,constructed based on the Chinese stock market data,negatively predict the market excess returns.As a crucial indicator of fear sentiment and systemic risk,the VIX attracts significant attention from both regulatory authorities and financial institutions.While previous studies have shown a positive link between VIX and future market excess returns,this relationship is notably absent in the Chinese context.As an alternative,Martin(2017 QJE)explores the price discovery ability of options and relates the market's expected return to its risk-neutral variance,proposing a modified index,the so-called SVIX,to measure the expected excess return.Furthermore,Martin(2017)finds that not only SVIX provides a lower bound for equity premium,but it is also close to its true value.In other words,the predictive coefficient of SVIX concerning the excess return of the US market is 1,providing a direct measure of the equity premium.However,our empirical results show that SVIX's predictive coefficient for the excess return of the Chinese stock market remains negative.Modern asset pricing theory posits that higher systematic risk should correspond to higher expected returns.Though it seems that VIX and SVIX can provide measurements of riskiness and the expected risk premium on the U.S.market,both fail to measure the riskiness of the Chinese Stock Market.The negative correlation between SVIX(VIX)and future excess return on the Chinese stock market challenges the risk-premium tradeoff principle.If one adopts VIX or SVIX to approximate the riskiness of the Chinese stock market,the more risk she bears,the less expected return she can obtain.Building on these insights,this paper instead extends Martin's(2017)framework into a more general setting to estimate the risk-neutral variance of excess returns.In theory,both the SVIX and VIX are designed to measure the uncertainty associated with risky returns.The VIX quantifies the risk-neutral entropy of the risky returns,while the SVIX provides an alternative measure of the risk-neutral variance.This duality justifies the common practice of adopting both indices as indicators of asset riskiness.However,both VIX and SVIX ignore the potential put-call parity violation.Though the violation of put-call parity tends to be minimal in the US market,our study reveals that the violation is significant in the Chinese stock market.Therefore,this paper extends the framework of Martin(2017)to characterize an approximated upper bound of the risk premium,not only taking the potential violation of put-call parity into account but also providing an approximation of risk-neutral variance estimation when the parity violation is not ignorable.Though it is straightforward to extend the estimation of risk neural variance to accommodate the potential violation of put-call parity,a direct result from this estimation is that the risk-neutral variance of the Chinese stock market can be negative if one adopts Carr and Madan's(2001)formula.For example,the mean value of this naive estimation of the risk-neutral variance of the Chinese stock market is-0.0952 from Jan 2016 to Jul 2017 and is-0.0807 from Feb 2020 to Jun 2020.Our theoretical analysis results in a more general index,called LVIX,where"L"stands for the market frictions,e.g.,liquidity constraints.Utilizing data spanning from January 2016 to December 2023 for China-sourced from Wind,and from January 1996 to December 2020 for the U.S.sourced from Option Metrics,we have uncovered several key findings:(1)the predictive coefficients of Rf,t→T·LVIX2t→T of SSE50 and S&P500 are both close to 1,confirming the theoretical derivation.In contrast,the predictive coefficient of Rf,t→T·SVIX2t→T is negative for the SSE50 though close to 1 for S&P500.(2)This predictive efficacy of Rf,t→T·LVIX2t→T remains robust even after accounting for various other predictive indices,including price-to-earnings ratios and realized returns.(3)When compared to a passive buy-and-hold strategy or an investment strategy predicated on SVIX,a strategy based on LVIX significantly enhances out-of-sample investment performance.Theoretically,the difference between LVIX and SVIX is tiny when the violation of put-call parity is minimal.However,SVIX is not proportional to the risk-neutral variance of excess return when violation of put-call parity is significant,in this case,LVIX remains to be proportional to an upper bound of the risk-neutral variance.In sum,our analysis reveals that LVIX offers not only a real-time measure of the risk premium but also a sophisticated,theory-driven method for assessing market risk.
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