1. Option volatility skewness and volatility "smile".
For traditional linear financial instruments, volatility represents the volatility of asset risk and can be used to measure the uncertainty of returnsOptions are non-linear financial derivatives instruments, and the rights and obligations faced by buyers and sellers are unequal, which makes options often more complex and changeable in terms of pricing and expectation judgment. In previous Options Focus series, we mentioned that the pricing of an exchange option contract is determined by five factors: the underlying**, the strike price, the time to expiration, the volatility and the interest rate. Among them, volatility is the most difficult and volatile abstract concept to observe, and the other four factors are relatively stable variables. With the development of the options market, the use of options for volatility trading has attracted more and more attention from investors, and this paper mainly analyzes options from volatility skewness, skew and other indicators.
The BS option pricing model assumes that option volatility is constant, but in practice** we see that implied volatility has a "smile" characteristic. This specific phenomenon reflects the fact that implied volatility can be skewed, that is, the distribution of random variables is asymmetrical. When the implied volatility distribution of each option deviates to the left relative to the standard normal distribution, a thick tail occurs, which we call a left skew. If a thick tail appears on the right side, we call it right deviation. As can be seen from option pricing theory, if the yield conforms to a standard normal distribution, then implied volatility is a constant and does not change with the change in execution**. However, if the return distribution is based on the standard normal distribution, with characteristics such as spikes and tail hypertrophy, then the function of implied volatility with respect to execution ** will show a certain skew. In real life, we find that the implied volatility of options is often different at the same expiration date and different strike prices, and has a certain degree of skew, which is collectively referred to as the volatility smile. Essentially, the shape of the volatility smile curve depends on the degree of deviation from the true probability distribution of the underlying asset's return. The actual probability distribution of returns is usually based on the three characteristics of "left tail hypertrophy", "right tail hypertrophy" and "bilateral tail hypertrophy" on the basis of the standard normal distribution, which also makes the shape of the volatility smile curve show three patterns: left-biased, right-biased and smiley.
Data: Research & Development Department of CCB.
Second, the volatility of options is skewed
2.1 Definition and classification of option volatility skew
Volatility skew describes the concept of relative quantitative comparison of hidden waves of different options. The implied volatility of options not only reflects investors' expectations of future volatility in options trading, but also expresses the supply and demand of options guided by emotions, and the degree of skewed volatility of options can reflect investors' supply and demand of options.
Volatility skew is further divided into horizon skew and vertical skew. Vertical skew shows the volatility skew of different executions** of options contracts with the same expiration date, and if the vertical skew is deviated, traders can perform volatility arbitrage by combining in-the-money and out-of-the-money contracts. While the horizontal skew shows the skew of the volatility of the expiration date of an option contract with the same execution**, traders look for opportunities by using the calendar spread to see the difference between the implied volatility of option expiration.
2.2 Calculation and characteristics of option volatility skew indicator
The formula for calculating the Volatility Skew Index (VSI) is as follows:
Among them, OTM options represent out-of-the-money options, and ATM options are at-the-money options. Considering the liquidity of options, at-the-money options are usually in-the-money or out-of-the-money option contracts. VSI can also be divided into call option VSI Call and put option VSI PUT when calculating.
The logic of the option volatility skew combination at the market trading level is based on finding the volatility of different options of the same underlying asset that are substantially different, which can be divided into positive and negative volatility slope trading, and it is necessary to maintain delta neutrality or set delta exposure in this trading portfolio. In specific transactions, it is also necessary to determine whether the current volatility is at an overall historically high or low level to make a judgment on the control of **.
2.2 Forward option volatility skew
The positive volatility slope refers to the higher the strike price, the higher the implied volatility, and the lower the strike price, the lower the implied volatility, that is, the right-biased structure of the volatility curve is shown as a curve sloping to the upper right in the graph with the ordinate as the volatility and the abscissa as the strike price.
When the iv of an option is a positive slope, since the volatility of the contract on the left side of the volatility curve is undervalued and the contract on the right is overvalued, we can use a combination strategy to buy contracts with lower valuations and sell contracts with higher valuations. For call options, it is the first in-the-money contract, selling out-of-the-money contract;For put options, it is an out-of-the-money contract and a sell in-the-money contract. Close the position when the slope of iv returns to the normal range.
2.4 Inverse option volatility skew
The negative volatility slope means that the higher the strike price, the lower the implied volatility, and the lower the strike price, the higher the implied volatility, that is, the volatility curve has a left-shifted structure. In the graph with the ordinate as the volatility and the abscissa as the strike price, it appears as a curve sloping to the lower right. When the iv of an option has a negative slope, because the volatility of the contract on the left side of the volatility curve is high and the volatility of the right contract is low, you can arbitrage by selling the left contract and ** the right contract. For call contracts, the ones sold are in-the-money contracts, and the ** contracts are out-of-the-money contractsFor put contracts, sell out-of-the-money contracts, and ** sell in-the-money contracts. When the slope of IV returns to the normal range, consider closing the position and exiting the market.
For the above-mentioned volatility bias trading logic, the trading portfolio used is delta-neutral, because the volatility arbitrage strategy mainly obtains volatility gains, and the exposure of directional positions is uncontrollable risk for the strategy, so the delta of the trading portfolio itself needs to be controlled in a certain proportion, which is logically a delta-neutral combination.
3. Introduction to the historical volatility cone of options
By dividing different levels of historical volatility, the option historical volatility cone is conducive to three-dimensional judgment of what level the current historical volatility is, and then analyzes the current implied volatility level to determine whether there is a volatility trading opportunity. The volatility cone shown in our chart is to statistically analyze the historical volatility data of the 20-day, 40-day, and 60-day targets of each period separately, that is, the data of the 20-day, 40-day, and 60-day historical volatility of the target in the past year, and find out the minimum, maximum, and 10% quantile (value % quantile (value % quantile (value % quantile (value % quantile (value).
By looking at the data of the historical volatility cone, we can determine the high and low position of the current volatility relative to historical levels. If the volatility of the current month contract has already exceeded the 75th percentile, it is in a higher position. Buyers of current month contract transactions need to pay attention to the risks brought by potential volatility regression, weigh whether the downside returns can cover the risks, and consider closing in time if they no longer expect to have a large upside down in the future. From the perspective of volatility cone, on the one hand, we can assist ourselves in judging the current volatility according to the historical quantile, and make corresponding volatility trading, or provide additional reference when trading directionally. On the other hand, we can trade the volatility of different maturities according to the relative volatility of different maturities. For example, if an investor thinks that the volatility of the next month's contract is too high, and the volatility of the next quarter's contract is too low, then he can sell the next month's at-the-money straddle portfolio, and at the same time ** the next quarter's at-the-money straddle portfolio, and then wait for the volatility to return to normal and then close the position.
Fourth, summary
Based on an in-depth analysis of the market volatility characteristics and the implied volatility structure of options, we construct the Volatility Skew Index (VSI) to describe the degree of skew of the volatility of options contracts. Through the observation of the VSI index, we find that the VSI index exhibits a mean reversion characteristic, and uses this feature to capture the arbitrage opportunities caused by the volatility deviation between different option contracts.
Traditional financial instruments can only use volatility to control risk, and options are a non-linear financial trading tool that can avoid risk and bring returns by directly trading volatility. Implied volatility has strong scalability because of its mean reversion characteristics. At the same time, in actual trading, the implied volatility of options is not constant, and the shape of the volatility curve will also show different shapes. Based on this characteristic, we have compiled the VSI index to express the IV difference between options contracts with different strike prices, that is, the degree of skewness of volatility.
We find that the VSI index actually exhibits significant mean reversion characteristics, and the calculated VSI index will quickly revert to around the average level after both the upward and downward deviation of the call contract. Using this feature, we can theoretically give a signal to open a position based on the deviation of the VSI index, and when the index reverts to the mean, we can close the position and make a profit. In fact, the VSI index describes the level of volatility between out-of-the-money and in-the-money contracts. When the VSI index breaks through the threshold upward, we can consider that the volatility of out-of-the-money contracts at this time is high, while the volatility of real-value contracts is low, so volatility arbitrage can be carried out by shorting out-of-the-money contracts and longing real-value contracts. The reverse is also true, in this strategy, in addition to creating trading signals, it is also necessary to pay attention to the control of positions, mainly the choice of volatility timing. The combination of trades needs to be delta neutral, which allows the portfolio to have exposed positions in the direction of volatility. When opening a position, we need to analyze the overall volatility of the market to determine whether the volatility situation at this time is conducive to the trading portfolio. Generally speaking, it is better to short volatility when volatility is high and short volatility when volatility is low. According to this logic, when the volatility of the market is favorable to the trading portfolio, we can take a ** trade, and when the volatility conditions of the market do not match our settings, we can take a semi-** trade to reduce the risk. The criteria for judging volatility are based on the combination of historical volatility and implied volatility data. Since the VSI index of the call contract is different from the put contract, the backtesting strategy needs to be carried out separately. The backtest results show that the put contract has a higher deviation rate and a higher strategy return, but the drawdown control is not ideal. The portfolio can adapt to market changes over a longer period of time, and the signal data can generate effective arbitrage opportunities, so that the investment strategy can achieve relatively stable profit results.