Options Greek Delta and Delta Neutral Trading Strategies

Option Greek Delta

is perhaps the most popular among the Option Greeks - Delta, Theta, Vega and Rho. This article will discuss Option Greeks Delta and especially some strategies called Delta Neutral trading strategies based on the concept of this Greek. If you are a beginner, you might first want to read my article on Understanding Stock Options through an example and Option Greeks for Beginners.

Definition of Option Greek Delta

Delta of a Call or a Put Option is defined to be the change in the price of that Option caused by a unit change in the price of the underlying (stock, index or commodity).

Example of Option Greeks Delta

Among Several factors which influence the price of the Option is the current market price of the underlying. Let us say for example you have bought a Call Option on a stock whose current market price is $50. The strike price of the Call Option is $55 and the price is $3. Now suppose immediately after buying the call option, the price of the underlying stock increases to $51. Naturally this will make the option more expensive. You observe this change increases the price of the Option from $3 to $3.3. Thus the delta of this Option is $0.3. This is exactly the change in the Options premium caused by unit change (in this case $1 change) in the price of the underlying stock.

Some remarks and Characteristics of Delta

1. Delta of a Call Option Option is positive varies from 0 to 1. Delta of a Put Option varies from -1 to 0. Thus Delta of a Call Option is always positive while that of a Put Option is always negative.
   
2. Delta of an deep In-the-money Call Option is one while that of a put Option is -1. This is because deep in the money Options tend to behave like futures.
3. Delta of At-the-money Options is higher in magnitude than Options which are far Out of the Money. Indeed far Out of the Money Options tend to have a delta closer to zero.
4. For a given Strike Price in an Option Chain, the sum of Delta of the Call Option and Put Option for that strike price is always equal to 1.
   
5. The price change in an Options Premium can be caused by several factors in combination to the price change in the underlying. To get an idea, in the above example suppose the price of the stock falls to $49 the next day. Consequently the price of the Call Option falls from $3 to $2.5. This drop may not entirely be due to the fall in the price and also may be a combination of other factors like time depending to expiry date reduces or change in Implied Volatility.

How to Calculate Option Greek Delta? What is the formula for calculating delta?

The Formula for calculating delta is a bit complicated. However you can download Options Calculator which can be used to calculate not only the price of an Option but also the theoretical value of all Option Greeks, Delta, Theta, Vega and Rho.

Delta Neutral Trading Strategies

There are Option strategies based on the concept of Options Greek Delta. This post will discuss two such strategies. They are very easy to understand.

1. Delta Neutral Strategy 1: Buying Delta Neutral Strangle - This strategy can be used when you expect the price of an underlying stock or index to fluctuate by a large amount in the near future. Buy a suitable Call Option and calculate its Delta. Then buy a Put option on the same underlying having the same magnitude of Delta. For e.g. if your Call option has delta equal to 0.5, then you should buy a put option with Delta -0.5. Thus the combined delta of both the Options is equal to zero. That is why this is called "Delta Neutral" strategy. The advantage of holding a Delta Neutral combination rather than buying a random Call and Put is that you lose very little even if you decide to square off or quit after a small fluctuation in the price of the underlying. You gain the price of the underlying, as expected changes by a large amount.
2. Delta Neutral Strategy 2: Writing a Delta Neutral Strangle - This strategy can be used in a stable stock market when the price of the underlying stock or index is not expected to fluctuate by a large amount. In this situation you sell a Call Option on the stock and also a Put Option whose delta is negative of the Delta of the Call Option. The strategy is then to sell such a Delta Neutral Combination, then square off after some time. As time remaining to expiry decreases, the price of the Options you wrote will decrease. Then you gain by squaring off because of the drop in price.
   

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