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Using the options Greeks to Enhance Hedging Strategies

Montréal Exchange
October 17, 2023
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In this third article of a four-part series, we explore the concept of option hedging using the ‘Greeks’, which are five variables in option pricing represented by letters of the Greek alphabet.

The variables are:

1. Delta: Measures the change in an option’s price for each \$1 change in the price of the underlying stock.
2. Gamma: Measures the change in delta for each \$1 change in the price of the underlying stock.
3. Theta: Measures the change in an option’s price for a change in its time to maturity.
4. Vega: Measures the change in an option’s price concerning a change in implied volatility in the market.
5. Rho: Measures the change in an option’s price for each 1% change in the risk-free interest rate.

To gain deeper insights into each of the Greek variables, you can explore the Option Matters blog for articles dedicated to this subject. Understanding the Greeks can significantly enhance your ability to navigate the world of options and make more informed and strategic investment decisions.

Delta hedging

Until now, we have yet to consider the option’s delta, a crucial variable that impacts the effectiveness of the protection put options can provide. The delta indicates the number of options required for ideal protection.

The following formula is used to calculate the number of options to buy:

Number of options to acquire = ( Number of shares in your possession / Option’s delta ) / 100

For example, suppose an investor holds 600 shares of company ABC and intends to determine the appropriate number of options to buy for protection against a drop in ABC’s share price. The investor has found an option with what they consider to be the appropriate strike price, and it has a delta of 0.65.

Number of options to buy = ( 600 / -0,65 ) / 100 = -9.23

In this scenario, the investor will need to purchase nine put options to protect 600 shares.

It is crucial for the investor to continuously monitor their position and adjust the number of options held based on any changes in the option’s delta. By using delta hedging, investors can improve their protection strategy and maintain a balanced and optimized portfolio throughout market fluctuations.

Gamma

Gamma is an option Greek variable that indicates how sensitive the option’s value is to market movements. It is an important variable to understand as it helps determine how often adjustments are required to maintain an optimal hedge.

Here are some key points to remember about gamma:

1. Higher Gamma: A higher gamma implies a more volatile delta and by default frequent adjustments to maintain a desired hedge.
2. Price Changes: At-the-money options experience faster price changes compared to out-of-the-money options.
3. Time Value Impact: Options close to the expiration date experience faster price changes than those with more time remaining.
4. Option Buyer Advantage: A high gamma is advantageous because it results in the option’s delta approaching 1 more quickly.
5. Option Seller Risk: Option sellers face risks when combining a high gamma with forecasting errors, as it can lead to faster value depreciation in the option.
6. Delta and Moneyness: The delta of an out-of-the-money option is closer to 0, while the delta for in-the-money put options approaches -1, and for in-the-money call options, it approaches 1.

Understanding gamma is crucial for both option buyers and sellers. It allows buyers to better optimize their position, while sellers must be mindful of the risks involved. By taking gamma into account, investors should be able to enhance their hedging strategies and perform better in changing market conditions.

Understanding theta to reduce time decay

Understanding theta is crucial to mitigate the impact of time value decay on options. By investing in options with a lower theta, investors will reduce the effects of time decay. Trading long-term equity anticipation securities (LEAPS) is another option to minimize theta exposure, although it may require a higher premium. More advanced strategies like calendar spreads and short condors can also be employed for time management, and explored further in the Guide & Strategies section on the Montréal Exchange website.

The misunderstood Greek

Rho is an often overlooked Greek variable due to its relatively small impact in options analysis. Rho is included in the Black-Scholes formula to account for the cost of carry associated with holding an asset, but for options, this cost is minimal.

Consult Using options to express market views and Protecting your portfolio through a volatile period, the first and second articles of a four-part series on using options as part of your portfolio management.

In no event will Desjardins Securities, its directors, officers, employees or agents be liable for any loss or damage suffered or expenses incurred as a result of the use of the information contained herein.

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