Lottery and bubble stocks and the cross‐section of option‐implied tail risks

Abstract

The options smile provides forward‐looking information about the risk at the center of the distribution (ATM‐IV) and at the tails (Skew). We investigate the cross‐sectional determinants of the options smile using indices that capture firm fundamental risks, heterogeneity in belief, lottery characteristics, and bubble characteristics. We find that at‐the‐money (ATM) volatility is explained mainly by historical risks and predicted future risks measured using accounting‐based risk measures and firm characteristics. However, the cross‐sectional variation in the skew is driven by risk premia and by buying and selling pressure, which is influenced by heterogeneity in belief and the underlying's lottery‐like and bubble‐like characteristics.

Belief distortion near 52W high and low: Evidence from Indian equity options market

“…To remove outliers, we winsorize all of our variables at the 1st and 99th percentile. The average Volatility RND for our sample is 0.38, which is very close to the average IV value of ATM options reported in the Indian market by previous studies (Agarwalla et al, 2022). The mean value of Skew RND is − 0.12, confirming the finding in the literature that option-implied RND is typically negatively skewed.…”

“…The SSO and SSF prices are obtained from the NSE trade book with matching time-stamped quotes, and the volume data are taken from the NSE BHAV files. Following Jain et al (2019) and Agarwalla et al (2022), we applied various filters to the options price data. First, we removed options contracts that traded for less than (any) 5 min on a day.…”

“…To estimate the volatility of ATM options and the slope of IV smile, we use time-matched high-frequency data from both options and futures markets. Before starting the IV estimation we clean the data by broadly following Jain et al (2019) and Agarwalla et al (2022). We first exclude all SSOs contracts that have traded for less than 5 min in a day.…”

“…India has liquid SSF market that allows us to use the Black (1976) model for IV estimation. Previous studies in the Indian market have used a similar method to estimate IV (Agarwalla et al, 2021a(Agarwalla et al, , 2021b(Agarwalla et al, , 2022Jain et al, 2019). The use of SSF price instead of spot price helps us to avoid the calculation of the cost of carry and dividend yield while doing IV estimation.…”

Role of derivatives market in attenuating underreaction to left‐tail risk

“…For this, we use the Fama and MacBeth (1973) regression, wherein we regress the monthly average of these variables over lagged IMIN and other control variables. Prior papers have found that stocks' market beta, systematic risk, BbyM , size, idiosyncratic skewness of the stock returns, analyst dispersion and coverage, put‐to‐call ratio, and momentum can explain the cross‐sectional variation in the ATM‐IV and IVSKEW (Agarwalla et al, 2022; Bollen & Whaley, 2004; Dennis & Mayhew, 2002; Duan & Wei, 2009; Feng et al, 2018). We have included these variables as control variables.…”