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The influence of 50 ETF dividend on option arbitrage strategy

submitted 2020-01-01 22:22:58

"Huaxia SSE50 ETF" will deliver dividend and be ex-dividend on December 2, 2019. On that day, 50ETF options will be adjusted accordingly, and the exercise price, contract unit and unit premium will be changed. What impact will these changes have on arbitrage trading? We will explain in this article:

(I) risk free arbitrage of IH futures

In the risk-free arbitrage of IH futures and 50ETF options, investors need to make the spot market value corresponding to long and short portfolio equal, that is, the contract value of stock index futures is equal to the spot market value corresponding to 50ETF options composite futures. IH futures will not be affected by the dividend of 50ETF. According to the first part above, the product of the price of 50ETF after ex dividend and the new contract unit of option will not be changed, and the spot market value corresponding to spot right will not be changed. Therefore, after the dividend of 50ETF fund, IH futures' risk-free arbitrage in the same period does not need to be adjusted.

(II) No risk arbitrage of 50ETF fund in the same period

Considering the difficulty of securities lending, the risk-free arbitrage mode of 50ETF is mainly to buy 50ETF funds and hold synthetic short positions. We use s and K to represent the closing price and option exercise price of 50ETF before dividend, s’ and K’ to represent the corresponding data after dividend, and δ to represent the dividend of each unit fund.

Before dividend:

Spot position: N*S

Option Position: N*(P-C)

After dividend, the position of 50ETF fund becomes:

Spot position: N*S’+N*δ

According to BS formula, after dividend, the premium of short futures per unit option becomes:

P’-C’=K’*EXP(-rT)*N(-d2’)-S’*N(-d1’)+K’* EXP(-rT)*N(d2’)-S’*N(d1’)

For the cumulative distribution of normal distribution: n (x) + n (- x) = 1, so after dividend adjustment: P’ - C’ = k’- s’, which means that after adjustment, each p’ – C’ corresponds to 1 unit -s’, 50ETF fund short position after ex dividend. Therefore, the spot corresponding to 50ETF and option portfolio is as follows:

Spot position match: N*S’+N*δ

Option Position match:-N’*S’

It means that after 50ETF dividend, the number of spot corresponding to the option portfolio is more, and investors can close some option contracts or buy a certain spot long. The specific adjustments are as follows:

 Spot position Dividend impact Adjustment needed(both is ok) Arbitrage between 50ETF fund and option 50ETF Underlying of option synthetic short side increase (1)close option position “position * cash dividend / ( underlying closing price before ex-dividend day - cash dividend)” share 50ETF option synthetic short side; (2) buy “old unit * cash dividend/( underlying closing price before ex-dividend day - cash dividend)” share 50 ETF fund by using the cash dividend

(III) Volatility trading: Greek letters and implied volatility changes

The ETF dividend will affect the Greek alphabet in three ways: the underlying price will be lower, the exercise price will be lower and the contract unit will be higher. Here, we omit the specific derivation and give the change results directly:

Delta after adjustment= old Delta * underlying closing price before ex-dividend day/( underlying closing price before ex-dividend day-cash dividend)

Gamma after adjustment= old Gamma * [underlying closing price before ex-dividend day/( underlying closing price before ex-dividend day-cash dividend)]^2

Basically, after dividend, the absolute values of Delta and Gamma increased, while Vega and Theta remained unchanged.

Due to the adjustment of option contract, the contract unit changes, and there is a difference between the adjusted unit and the standard unit, 10000, so that while the exercise price is almost the same, and there is still a certain difference between the standard contract and the adjusted contracts and it cannot be arbitraged by 1:1 match. Therefore, the implied volatility of the adjusted option may be different from that of the standard contract.

Taking what happened in 2016 as an example, we selected 40 groups of contracts with similar exercise prices and adjusted contracts, and calculated their volume weighted average implied volatility. The results are shown in the figure below. In general, the implied volatility of the adjusted contract is slightly higher, with an average of 0.4 percentage points.

From a more detailed point of view, we can see that in the process of implied volatility changes, the "burr" of adjusted contracts is relatively more.

As a whole, after dividend, the Greek letters of options will change, Delta and Gamma will rise, Vega and Theta will remain unchanged, and the change of Greek letters above the second level will be more complicated; the implied volatility of the adjusted contract may also be different from that of the standard contract. These two factors will increase the analysis difficulty of volatility arbitrage. Combined with the decrease of liquidity of the adjusted contract, it is suggested that investors change positions into standard contracts.

50ETF分红对期权套利策略的影响
“华夏上证50ETF”将于2019年12月2日分红除息，当天50ETF期权将发生相应调整，行权价、合约单位、单位权利金都会改变。这些变化会对套利交易造成什么影响？我们在本文中予以说明：
（一）IH期货同期权无风险套利

（二）50ETF基金同期权无风险套利

（三）波动率交易：希腊字母与隐含波动率变化
50ETF分红会从三个方面影响希腊字母：标的价格降低、行权价降低、合约单位上升。在此，我们略去具体推导，直接给出变动结果：