Gamma-delta neutral option spreads – Carswellfamilyfoundation

Have you found strategies using option theta decay that are attractive, but you cannot bear the risk involved? At the same time, conservative strategies such as cover call a letter or synthetic letter about covered calls may be too restrictive. gamma–delta neutral distribution may be the best middle ground when looking for a way to use time decay while neutralizing the effect price action from the value of your position. In this article we will introduce you to this strategy.

Options “Greeks”

To understand the application of this strategy, knowledge of basic Greek measures is important. This means that the reader must also be familiar with the options and their characteristics.

Theta

Theta is the rate of decline in the value of an option that can be attributed to the passage of one day. With this spread, we will use theta decay to our advantage to profit from the position. Of course, many other spreads do the same thing; but as you will discover, hedging pure gamma and pure delta of our position, we can safely maintain the neutral direction of our position.

Strategy

For our purposes we will use ratio call text strategy as our main position. In these examples, we will buy options at a lower price. strike price than the price at which they are sold. For example, if we buy calls at a strike price of $30, we will sell calls at a strike price of $35. We will use the normal call writing strategy and adjust the ratio at which we buy and sell options to essentially eliminate the net gamma of our position.

We know that the proportional option writing strategy sells more options than it buys. This means that some options have been sold.”nakedThis is inherently risky. The risk here is that if the stock rises enough, the position will lose money as a result of the unlimited upside risk with naked options. By reducing the net gamma to a value close to zero, we eliminate the risk of the delta shifting significantly (assuming this only occurs in a very short time frame).

Neutralization of gamma radiation

To effectively neutralize gamma, we first need to find the ratio at which we will buy and write. Instead of looking for a relationship through a system of model equations, we can quickly figure out gamma neutral ratio by doing the following:

1. Find the range of each option.

2. To find the number you will buy, take the gamma of the option you are selling, round it to three decimal places, and multiply by 100.

3. To find the amount you will sell, take the gamma of the option you are buying, round it to three decimal places, and multiply by 100.

For example, if we have a $30 call with a gamma of 0.126 and a $35 call with a gamma of 0.095, we would buy 95 calls at $30 and sell 126 calls at $35. Remember this is price per share and each option represents 100 shares.

Buying 95 calls with a gamma of 0.126 is a gamma of 1197, or: $\begin{aligned} &95 \times ( 0.126 \times 100 ) \\ \end{aligned}$

Selling 126 calls with a gamma of -0.095 (negative because we’re selling them) represents a gamma of -1197, or: $\begin{aligned} &126 \times ( -0.095 \times 100 ) \\ \end{aligned}$

This adds up to a net gamma of 0. Because gamma is not typically rounded to three decimal places, the actual net gamma may differ by about 10 points from zero. But since we are dealing with such large numbers, these changes to the actual net gamma are not significant and will not affect the good spread.

Neutralization of Delta

Now that we have the neutralized gamma, we will need to make the pure delta zero. If our $30 calls have a delta of 0.709 and our $35 calls have a delta of 0.418, we can calculate the following.

95 calls bought with a delta of 0.709 is 6735.5, or: $\begin{aligned} &95 \times ( 0.709 \times 100 ) \\ \end{aligned}$

126 calls sold with a delta of -0.418 (negative since we sell them) equals -5266.8, or: $\begin{aligned} &126 \times ( -0.418 \times 100 ) \\ \end{aligned}$

The result is a net delta of positive 1468.7. To make this net delta very close to zero, we can short 1469 shares of the underlying asset. This is because each stock has a delta of 1. This adds -1469 to the delta, making it -0.3, which is very close to zero. Since you can’t short parts of a stock, -0.3 is as close as you can get to zero for a net delta. Again, as we stated in gamma, since we are dealing with large numbers, it will not be large enough to affect the outcome of a good spread.

Theta Research

Now that our position is essentially price neutral, let’s check its profitability. The $30 calls have a theta of -0.018 and the $35 calls have a theta of -0.027. It means:

95 calls purchased with a theta of -0.018 equals -171, or: $\begin{aligned} &95 \times ( -0.018 \times 100 ) \\ \end{aligned}$

126 calls sold with a theta of 0.027 (positive because we sell them) is 340.2, or: $\begin{aligned} &126 \times ( 0.027 \times 100 ) \\ \end{aligned}$

The resulting net theta is 169.2. This can be interpreted as your position earning $169.20 per day. Because options behavior does not adjust daily, you will have to hold your position for about a week before you can notice these changes and profit from them.

Profitability

Without going through everything admission requirements and clean debit and loans, the strategy we’ve described will require approximately $32,000 in capital. If you held this position for five days, you could expect to earn $846. That’s 2.64% on top of the capital required to create it – a pretty good return in five days. In most real-life examples, you will find that a position held for five days will generate a return of around 0.5-0.7%. This may not seem like much until you change the annualized return to 0.5% over five days – that’s a return of 36.5% per year.

Flaws

There are several risks associated with this strategy. First, you’ll need a low commissions to make a profit. This is why it is important to have a very low level commission broker. Very large price movements can also throw things off track. If held for a week, the necessary rate adjustments and delta hedging are unlikely; if you hold it for a longer time, the stock price will have more time to move in one direction.

Changes in implied volatilitythat are not hedged here may result in sharp changes in the value of the position. While we have eliminated relative daily price movements, we face another risk: increased exposure to changes in implied volatility. Within a short time time horizon Over the course of a week, changes in volatility should play a small role in your overall position.

Bottom line

The risk of writing odds can be reduced mathematically hedging certain characteristics of optionsalong with an adjustment to our position in the basic ordinary shares. By doing this, we can profit from the theta decay of the written options.