This is the first paper that concentrates on the FXI options market and documents the empirical characteristics of the IV smile of FXI options. In 2001, when it was first launched, the index consisted of the 25 Chinese stocks with the largest capitalization traded on the Hong Kong Stock Exchange. The FXI tracks the performance of the FTSE China 50 index very closely, as can be seen in Figure 1.
From reading the news on Chinese stocks, it is clear that the FXI is a reflection of investment opportunities in China's economy. In this paper, we first study the form and dynamics of IV FXI options. Further, inspired by Zhang and Xiang (2008), we believe that IV curve factors are good proxies of risk-neutral moments.
There is also a vast body of literature attempting to explain the causes of the shape of the IV curve (Garleanu, Pedersen, and Poteshman (2009); , to quantify the IV of the FXI options and for predictive regressions. The newly included 25 stocks accounted for only 6.76% of the total trade day weights.
Moneyness
The left side represents the actual growth of one stock based on discretely paid dividends, while the right side represents the equivalent growth represented by a continuously paid dividend. The market ATM strike price K0 is closest to Ft,T for each term and each day. Following Carr and Wu (2003), the methodology used by CBOE in calculating the VIX index and market practice, we select the IV of out-of-the-money options to calculate the IV curve of FXI options to display.
An out-of-the-money option is normally more liquid and model-sensitive than an at-the-money option, and is therefore widely used when examining IV curves by investigators, researchers, and exchange holding companies, such as the CBOE. For put options we select those whose prices are less than the strike price, i.e. K < Ft,T, and for calls we select those whose prices are greater than the strike price, i.e. K > Ft,T .
Quantifying Implied Volatility
Predicting FXI Returns
Xt is one of the predictors, that is, the level, slope, curvature, third and fourth cumulants, or first differences of these predictors, at the end of the month. In addition to the in-sample regressions, we also test the out-of-sample predictions for FXI monthly excess returns. The evaluation sample is considered an important parameter in terms of the power of the prediction evaluation tests (Welch and Goyal (2007), Rapach, Strauss and Zhou (2010), Hansen and Timmermann (2012) and others).
The null hypothesis is that unconditional forecasting is not inferior to conditional forecasting (Welch and Goyal (2007)). We also define the initial evaluation ratio of the evaluation sample as ρand setρ= 1/3 and 1/2 following Ruan and Zhang (2018). In this section, we report and discuss the results of quantifying IV curves of FXI options.
Following the above method, we plot the fitted IV curves for each available maturity each day to study the dynamics of the IV FXI option by examining the resulting level, slope and curvature factors. We then calculate constant maturity IV factors to further study the FXI IV term structure and its time series dynamics. Finally, we conduct an empirical test of the FXI return predictability of the quantified IV factors.
Dynamics of the Quantified IV Curve
In general, the exact ATM IV (level factor) is positive and the curves tend to be negatively sloping with some positive curvature (convexity), i.e., a smiley shape as found for S&P 500 options by Carr and Wu (2003), Foresi and Wu (2005) and Fajardo (2017), among others. Therefore, the level is mostly positive and the slope is mostly negative, while the curvature varies between positive and negative values. The mean term structures of Ft,T and the level are upward sloping, and in contrast, those of the slope are downward sloping.
The manual curvature structure also slopes downward until time to maturity exceeds 360 days, after which it increases dramatically. The standard deviations of Ft,T and factors increase with maturity, except for the rate, which shows a decreasing trend across maturity categories. This decrease in the standard deviation of the level with larger maturities may be an indication that the exact mean reverts to the ATM IV, which is consistent with the general finding that the implied volatility of US ATM stock options is mean reverting (Dueker (1997); Fouque, Papanicolaou, and Sircar ( 2000); Higgs and Worthington (2008)).
The proportion of significant coefficients for ATM IV is always 100%, while the proportion of the slope decreases as the maturity increases and for the curvature has decreased very dramatically when the time to maturity is more than 360 days. Overall and for each maturity group, they are close to 100%, indicating that our quantification of FXI IV is reliable. However, we can observe that the quality of fit (R2) decreases slightly as maturity increases, which may be due to a decrease in trading activity and less consistent views of different options traders on long-term volatility.
Constant Maturity Quantified IV Curve
In Figure 9 (e), we can see that the curvature tends to be slightly positive in most cases and options with longer maturity IV, the inflection points are larger and more frequent. Turning to the difference in the 180- and 30-day factors in Figure 9 (b), (d) and (f), we can see that the short-term structures of the level (ATM IV), slope and curvature are usually downward sloping, downward sloping and flat, respectively. However, the level (ATM IV) experiences a period of extremely steep downward thermal structure during the GFC.
In summary, we can observe that the level is always positive overall and has a fairly flat term structure, that the slope is negative and has a downward sloping term structure and that the curvature fluctuates around zero with a downward sloping term structure for a duration of less than than 360 days. Levels appear to be turning, with prolonged periods of heightened volatility during the financial crisis, the recovery period and the recent depression in China. The level, slope, and curvature time series usually fluctuate around a positive, negative, and slightly positive value, respectively, with times of peaks.
Predictability of FXI Returns
We then extend the methodology in Zhang and Xiang (2008) and calculate constant maturity factors of IV FXI options to examine the term structure and dynamics of the factors. First, we divide the IV curve factors into groups by maturity to analyze the factor term structures. The thermal structure of level and slope is upward and downward, respectively, and that of curvature is downward sloping until the maturity is more than 360 days, after which it increases drastically.
The standard deviation of the level is decreasing across the maturity categories, while others are increasing, which may mean that the ATM IV mean is regressing over the sample. From the fitted IV curves using the average constant maturity factors, we can clearly observe the IV smile of the FXI options. To examine the time series dynamics of the FXI IV curve, we plot the 30-day and 180-day dynamics and find that the 30- and 180-day levels have a similar shape with periods of high volatility related to the Chinese and global economy, indicating , that investors expect similar volatility in FXI returns.
The slope and curvature are mostly negative and slightly positive, but the 180-day peaks are larger and more common. The term structures of the difference between the 180- and 30-day levels (ATM IV) and the slope slope downward, while that of the curvature is flat. Further explanation of the fluctuation of the factors over time is necessary, and further investigation into the determinants of these fluctuations in the time series would be of interest in our future work.
Finally, we test the predictability of FXI monthly excess returns using the factors, which represent the risk-neutral volatility, slope and skewness, and the risk-neutral third and fourth cumulants, their first differences. We find that the first differences of the third cumulants can predict future monthly FXI excess returns significantly in both in-sample and out-of-sample regressions. Chatrath, Arjun, Hong Miao, Sanjay Ramchander, and Tianyang Wang, 2016, An examination of crude oil flow characteristics: Evidence from risk-neutral moments, Energy Econ.
Shiu, Yung-Ming, Ging-Ginq Pan, Shu-Hui Lin and Tu-Cheng Wu, 2010, Impact of net buying pressure on changes in implied volatility: before and after the onset of the subprime crisis, Journal of Derivatives 17, 54–66. Skiadopoulos, George, Stewart Hodges and Les Clewlow, 2000, The dynamics of the implied volatility surface of the S&P 500, Review of Derivatives Research 3, 263–282. This table lists the sector classification of 50 individual stocks and the corresponding group weightings of the FTSE China 50 Index as of April 30, 2018.
The percentage of significant coefficients is the percentage of parameter estimates that are significant at the 5% significance level. This table reports summary statistics of the fitting results overall and for constant maturities of and 360 days, which are calculated by interpolating and extrapolating the estimated coefficients and factors. This chart illustrates the daily total volume and open interest for the FXI options market from October 19, 2004 to April 29, 2016.
