The risk factors of options are complex, among which the price-related risk indicators are Delta and Gamma. When hedging the risk of OTC options, Delta hedging is mainly used, that is, the Delta value of OTC options positions is calculated, and the overall Delta value is close to zero through floor trading, so that it is not affected by the overall small-scale fluctuation of the underlying price. For example, if the Delta value of OTC option positions is -0.5, the total scale is 2,000 tons of cotton, and the total Delta value is-1 1,000, the target price will increase by 1 yuan, and the OTC option will lose 1 1,000 yuan. In order to hedge the Delta risk, it is necessary to establish a Delta position of 1 1,000 yuan in the OTC market.
Delta neutral hedging can protect the overall position from small fluctuations in the underlying price, but it cannot be done once and for all. Because the Delta value of the option itself is affected by the change of the underlying price, with the change of the Delta, in order to keep the Delta neutral, it is necessary to conduct corresponding on-site trading. The change speed of δ is determined by γ. When the Gamma is too large, in order to maintain the neutrality of Delta, frequent on-site hedging transactions may be needed, especially in the case of open position gap, which may cause great risks. Before the listing of cotton options, the only on-site tool that can be used to hedge cotton off-exchange options is cotton futures, which has linear profit and loss characteristics and does not have gamma property. Therefore, in order to hedge the gamma risk of OTC options, it is necessary to use OTC options in the hedging process.
On-site options and off-site options have the same Gamma attribute, so on-site options can be used to hedge the Gamma risk, while the remaining Delta risk can be hedged by futures. The following are examples of hedging Gamma and Delta risks. If the current cotton price is 15000 yuan/ton, the Delta value of OTC option position is 0.48, the Gamma value is -0.0006, the contract size is 1000 ton of cotton, and the opening price is 250 yuan/ton. Assume that the Delta value of the put option used for hedging is -0.49 and the Gamma value is 0.0007. In order to hedge gamma, I bought the 17 1 hand option at the price of 2 18 yuan/ton. After buying floor options, the total Delta of floor options is 6 1, so it is necessary to short 12 cotton contract to hedge its Delta risk. If you simply use futures Delta hedging, you need 96 empty futures. The next day, if the underlying cotton futures opened with a gap of 400 points, the off-exchange option price rose to 483 yuan/ton, and the on-exchange option price rose to 463 yuan/ton. The following table analyzes the profit and loss of the two hedging methods in the case of opening gap. Option data is theoretical data, regardless of handling fees. It can be seen that the use of on-site options can effectively protect off-site options from the risk of target opening gap.
The above example shows the advantages of using floor options to hedge when the underlying assets fluctuate greatly. Because buying the floor option hedges the Gamma, the sensitivity of the overall Delta change is reduced, which can reduce the frequency of the adjustment of the floor contract position and help hedge the fluctuation risk. However, compared with Delta, adding floor option hedging needs to track multiple indicators and contracts, which requires higher calculation and operation requirements. Although hedging through floor options can obviously reduce the overall loss of hedging when the market fluctuates greatly, call options will also face the loss of time value, which will increase the hedging cost when the underlying price fluctuates little. Generally speaking, floor option can optimize the hedging scheme and strengthen the ability to control risks.