Gamma hedging

Gamma hedging
See also
Net Volume Vomma Selling Into Strength Three white soldiers Long put Zomma Long Hedge Overbought oversold indicator Decline ratio

Gamma hedging allows investors to mitigate risk related to changes of an option's delta. Delta defines expected change in price of the option related to change of asset value. Delta tends to change very fast, which is not convenient. Gamma shows rate of delta change in relation to asset value (in fact is twice calculated rate of change of the asset). The gamma changes more smoothly and allows investor to make better decisions. In order to optimize the strategy, investors usually use both delta and gamma hedging. For example, investor can buy call options and short shares based on delta and add another short at different level to protect against large delta.

Gamma (Γ) measure the change of the option's delta with respect to the underlying asset price. It can be defined by the second part of the price asset price. Suppose the gamma has a value of 0.8, it means 1 cash unit increase in the stock price will increase the delta of the option by 0.8. A 1 cash unit decrease in the stock price will decrease the delta of the option by 0.8. If gamma is small, it means the change of the delta is slowly with changes in the underlying asset price, so the adjustments to keep the delta neutral need to be made only relatively infrequently. If gamma is big, that is the delta is very sensitive to the underlying asset price, so it is risky to leave a delta-neutral portfolio unchanged for any length of time. High gamma means, that variations in delta are high, and hence more frequent balancing to maintain low delta exposure. Delta hedging is based on small changes during a very short time period, assuming that the relation between option and the stock is linear locally. When gamma is high, the relation is more curved than linear, and the hedging error is more likely to be large in the presence of large moves. The gamma of a stock is zero. We can use traded options to adjust the gamma of a portfolio, but when we thinking aout large moves, it is better to try something else.

"Pinning" a stock approaching expiry

It is possible to "pin" by Gamma Hedging a stock approaching expiry. If an investor with long gamma can delta hedge by sitting on the bid and offer, this trade can pin an underlying to the strike. If we are selling when the stock rises above the strike, and buying when the stock falls below the strike, it can be the negative effect. Important thing is, that amount of buying and selling has to be compared with traded volume of the underlying, so pinning is the best thing, when stocks are relatively illiquid or when the position is particularly sizeable. Given the high trading volume of indices, it is difficult to pin a major index. The biggest chance for pinning is when market is calm, because there is no strong trend to drive the stock away from its pin. Pin risk take place when the market price of the underlier of an option contract at the time of the contract's expiration is close to the option's strike price. In this situation, the underlier is said to have pinned. Seller risks, because he can't predict if the option will be exercised,so the seller cannot hedge his position and can loose or gain. An option position can result in an undesired risky position in the underlier immediately after expiration.

Examples of Gamma hedging

1. *The most common example of gamma hedging is done by traders who use delta neutral strategies. These traders will adjust their positions in the underlying asset to offset the changing delta of their options. For example, a trader might buy a call option with a delta of 0.5. As the underlying asset increases in price, the delta of the option would increase and the trader would need to buy more of the underlying asset to maintain a delta-neutral position.
2. *Another example of gamma hedging is the use of options with different strike prices and expirations. This is often referred to as a “spread”. The trader will buy one option with a higher strike price and sell one with a lower strike price. This can be done with both calls and puts. The goal is to reduce the gamma exposure by offsetting the delta of the two options.
3. *Finally, gamma hedging can also be done with futures contracts. By buying and selling futures contracts, a trader can offset the changing delta of their options by taking a long or short position in the futures market. For example, a trader might buy an at-the-money call option and then take a short position in the corresponding futures contract. The futures position would offset the changing delta of the call option.

Advantages of Gamma hedging

Gamma hedging is a popular risk management tool used by market participants to manage the risks associated with changes in the delta of an option. The following are some of the advantages of gamma hedging:

• It helps investors to maintain a neutral delta position over a period of time, thus reducing the risk of significant losses due to large swings in delta.
• Gamma hedging is also useful in reducing the effect of time decay on the option's value.
• Furthermore, gamma hedging helps to reduce the cost of hedging by allowing investors to adjust the hedge rate as the delta of the option changes.
• Additionally, gamma hedging allows investors to maintain their desired level of exposure to a given market while minimizing the risk of large losses due to unexpected market movements.

Limitations of Gamma hedging

A Gamma hedging approach has the following limitations:

• It is complex and time-consuming to perform the calculations correctly, and requires the investor to have a deep understanding of the underlying asset and the options market.
• Gamma hedging requires constant re-calculation of the delta, leading to increased costs and complexity.
• There is no guarantee that the hedging strategy will be successful; the hedging decisions may prove costly as the market price changes faster than the delta can be re-calculated.
• Gamma hedging can lead to large losses if the market moves in a different direction than expected, as the delta may not be re-calculated in time.
• It may be difficult to find the appropriate instruments to hedge the underlying asset.

Other approaches related to Gamma hedging

One-sentence introduction: There are several other approaches related to gamma hedging that allow investors to mitigate risk.

• Delta hedging - This approach involves the adjustment of a portfolio of options and the underlying asset to offset the position’s delta with the goal of maintaining a constant delta.
• Volatility hedging - This approach involves managing the volatility of an option portfolio by buying or selling options in order to limit the risk of large price swings.
• Theta hedging - This approach involves buying and selling options in order to hedge against the time decay associated with options.
• Vega hedging - This approach involves managing the sensitivity of the option portfolio to changes in volatility.

In summary, there are several other approaches related to gamma hedging that allow investors to mitigate risk, such as delta hedging, volatility hedging, theta hedging, and vega hedging.

References

• Andriot, A., Nirascou, P., (2013). Market’s gamma hedging absorption capability for barrier options. 05/12/2013.
• Benchaphon, C., Chutima, K., Apiwat, P., Thanasunun, S., (2008). Hedging with Options. October 6, 2008, Västerås.
• Jarrow, R. A., & Turnbull, S. M., (1994). Applied Mathematical Finance. Delta, gamma and bucket hedging of interest rate derivatives, 1(1), 21-48.
• Wu, L., (2005). Options Markets"P&L Attribution and Risk Management".

Footnotes

Author: Maja Rogalska