We find that the assumption that the underlying asset is perfectly positively (negatively) correlated with call (put) options does not hold in the Chinese options market. Such high barriers to the market have limited retail investor participation in the options market. In the options market in China, the options chain is created by the exchange with the following rules: For all new options (short/long) first offered in the market, there are at least two out-of-the-money (OTM) options, one at-the -money (ATM) option and two in-the-money (ITM) options with a strike interval of 50 points (100 point interval if the SSE 50 index is above 3,000 points) in the SSE 50 index.
The SSE adjusts the options chain according to the index; investors can trade options in the options chain. According to SSE's 2017 Annual Options Trading Report (2017), most options investors in China's options market are Class III investors. New options will be created along with the rise/fall of the underlying asset in the option chain.
Black-Scholes option price and the market price
In this section, we report the detailed result of the calculated Black-Scholes price compared to its market price in the SSE 50 option. The Black-Scholes option price is calculated from its risk-free rate, the daily spot price of the underlying asset, volatility, dividends, and the option's time to maturity. We then calculate the average difference between the market close and the Black-Scholes price.
While for the put options, the average time value from the market price is higher than the time value from the Black-Scholes price mainly with a large number of long-term Deep-ITM/ITM options. Consistent with the price comparison in Table 4, the time value of other groups is slightly lower than the time value from Black-Scholes. The implied volatility is calculated from the market price with other known variables in the Black-Scholes formula.
The perfect correlation in the Chinese option market
On the one hand, we find that the average implied volatility of call options is significantly lower than the historical average annual volatility. On the other hand, the mean implied volatility in the put options is significantly higher than the historical mean annual volatility, all of which are consistent with the findings in Table 4. We find that there is no perfect correlation in the two call options (that ie, not 1 in the call and not -1 in the put with the underlying asset).
However, in the Deep ITM option, the market price and the change in the underlying asset are much closer to perfect correlation. Correlation in the entire call (put) sample does not support the assumption of perfect correlation in the one-dimensional diffusion model. In the subgroup test, we find that the Deep in the money option and the short-term option have a higher correlation ratio compared to the other groups.
Monotonicity in the Chinese option market
In the money subgroup tests, the Deep In The Money option group has the lowest violation. In contrast to the rapid growth in trading volume and market participation, the percentages of Type I offenses did not decrease in the following months3. In the money subgroup test, the type I violation rate in the Deep In The Money option is lower than that for the other groups.
Similar to the call option, the type I violation ratios did not decline in later months with improved daily trading volume. A violation data matrix is formed with two new variables to inspect the type II violation: A1 = ∆S ∗∆C and A2 = ∆S∗∆P. We select the options data by excluding the five trading days with no change in the underlying asset's price during our data sample period.
The violation rate in the Deep-OTM group is higher than that of the other moneyness groups. We find that the average breach rate in type II is lower than the average S&P 500 options market (4.25%). The type II violation rate in the OTM group is higher than that of the other moneyness groups.
We take only these five trading days from our entire sample for type III violation test. We formed the sample by selecting all trading days with 0% return in the underlying asset. We exclude these five trading days' data from our entire sample for the type IV violation test.
The overadjustment ratio is the lowest in the Deep-OTM group among all options.
The delta-hedged gain analysis
If there is only one risk factor in the options market, the hedged portfolio must have zero excess profit. On the other hand, if some other risk factors exist, the underlying portfolio of the hedged asset must have non-zero returns. We can conclude that there are other risk factors in the Chinese options market such as Xt as we have illustrated above.
Following the methodology of Bakshi and Kapadia (2003) in examining the delta-hedged profit of options, we form the option-delta-hedged portfolio as follows: A put option is bought at the daily settlement price Pt. 2) The call (put) options are discreetly hedged with the underlying asset (short/long) until their expiry date: t+τ. Stn+1 is the price of the underlying asset at time t+ ∆t, ∆tn is the smallest rebalancing frequency, which is one day in our test.
The average loss (profit) in each portfolio measured at the initial price of the underlying asset is 0.6% or 4.97% measured at the initial premium of the call option. The average loss (profit) in each portfolio measured at the initial price of the underlying asset is -1.28% or -2.38% measured at the initial premium of the put option. Compared to Bakshi and Kapadia's (2003) delta-protected profit test, the delta-protected profit in the Chinese options market is generally higher (lower) than in the S&P 500 call (put) option market.
For example, the average delta-hedged profit in the S&P 500 short-term ATM call option is about -0.13% (as a ratio of the initial call premium), while the average profit short-term option in the Chinese call market is 3.25%. According to Table 18, the explanatory variables: Vega, Intra-volatility and investors' adjustments to open interest contributed the most to the non-zero delta hedged profit. According to table 18 in ATM put group, the explanatory variables vega, intra-volatility, Short sale volume in total volume and option's price change contributed the most to the delta hedged profit.
Since vega and intra volatility are related to non-permanent volatility, investors in the Chinese options markets are trading with several other risk factors related to volatility in that market.
Dividend adjusted effects and non-standard option
We inspect fixed effect and random effect in each group according to the Hausman test, and we choose a fixed effect model in our panel regression. After each dividend payment, all existing options' strike price/exercise units will be adjusted to maintain their pre-dividend notional value. The custom options have non-standard strike price/exercise units compared to standard options (50-point strike interval and exercise unit of 10,000).
Non-standard option chains will not adjust along with changes in the price of the underlying asset; are less efficient and illiquid compared to these standard options. Compared to standard options, the non-standard options chain will not add a new strike along with the movement of the underlying asset, which may lose its strike ATM in favor of the underlying asset. According to Table 19, non-standard call and put options are less actively traded than standard options.
Both non-standard calls (puts) generally trade below their Black-Scholes price, which is somewhat different from our main results. Our research focuses on whether the one-dimensional diffusion model is applicable to the developing index options market in China. This suggests that arbitrage can be performed by short-selling positions in put options and taking a long position in short-term call options.
As for the basic assumption in the one-dimensional diffusion model, they are violated in the options market in China, especially in those groups of long-term money and Deep OTM. The non-zero delta-protected profit in the option sample indicates that option traders in the Chinese options market are trading with some other risk factors related to volatility and not just fundamental risk. In the money pools subtest, ITM options are generally more efficient than options in other pools.
Significant non-zero delta-hedged gains and arbitrage profits from the Black-Scholes price suggest that the one-dimensional spread model does not apply to the SSE 50 index options market in China.
The dividend adjustment in the Chinese option market
Results are grouped by full sample filtered money supply at-the-money (ATM)/in-the-money (ITM)/Deep-in-the-money (DITM)/out-the-money (OTM)/Deep-out-the -money (DOTM) groups and options maturity. Results are grouped by full sample filtered money-at-the-money (ATM)/in-the-money (ITM)/Deep-in-the-money (DITM)/out-the-money (OTM)/ Deep-out-the -money (DOTM) groups and options maturity. Results are grouped by full sample filtered money supply at-the-money (ATM)/in-the-money (ITM)/Deep-in-the-money (DITM)/out-the-money (OTM)/Deep-out-the -money (DOTM) groups and options maturity.
(DHG/S0)% measures the delta-hedged gain by the percentage of the original underlying asset price S. The results are grouped by full sample, filtered money volume at the money (ATM)/in the money (ITM) /Deep-in-the -money (DITM)/out-the-money (OTM)/Deep-out-the-money (DOTM) groups and option maturity in call options. (DHG/S0)% measures the delta-hedged gain by the percentage of the original underlying asset price S.
Results are grouped by full sample, filtered moneyness moneyness at-the-money (ATM)/in-the-money (ITM)/Deep-in-the-money (DITM)/out-the-money (OTM)/Deep - out-the-money (DOTM) groups and maturity terms of options in put options. OI Chg% is the option's daily percentage change in total open interest; Spot chg is the variation of the underlying asset on the spot market.
