Joey

April 13, 2022

**Introduction on Greeks: Delta**

**Definition of Delta**

Delta by definition is the rate of change in an option’s theoretical value given a unit change in the price of underlying asset. It measures the price sensitivity of an option to its underlying asset.

**Four dimensions to understand Delta**

Delta can be illustrated from four dimensions:

Fundamentally delta calculates the coupling coefficient and the price sensitivity of an option to its underlying asset. A long call option with delta value of 0.6 means that the option value would rise 0.6 dollar per stock when the underlying equity rises 1 dollar per unit. As the price change of an option would not surpass the price change of its underlying asset, delta is always valued between -1 and 1.

Delta also estimates the number of shares traded when we are betting on an option market. Suppose a trader bought an option contract of one lot with delta equals to 0.6, this trade equals to a long position size of 60 stocks of direct buy-in on the equity market. Whereas compared with direct trades on the equity market, option trading can be more cost-efficient with less total of premium and commission required than purchasing shares. Though the offset can be higher risk exposure under leverage, option trading offers investors chance to bet on stock price with less cost.

Delta can tell the direction of the bet. A long call or short put has a positive delta. It means the option price is moving at the same direction of the equity price. A short call or long put has a negative delta, which means the option price would move to the opposite direction of the equity price.

The final most important property of delta is that it can indicate the probability of an option strike price being in ITM (in-the-money). In other words, it measures the winning chance of an option bet. A buy-call option with delta value higher than 0.5 has a higher chance of being ITM at the expiration. On the opposite, a buy-call option with delta value lower than 0.5 is more likely to be OTM at the expiration. The figure below describes relationship between delta value and a higher chance of being ITM or OTM at the expiration.

Figure 1: delta value and the probability of being ITM or OTM

Delta can be also affected by time value that an option with longer dates to expiration has higher uncertainty over future price direction. While on the opposite, tighter time to expiration leaves less breath for final option price to change. The closer we get to date of expiration, more definite we are sure of the strike price being in ITM or OTM. Therefore, delta value will ultimately progress to either 1 or 0 at the expiration.

**Why is delta important?**

The primary role of delta, as said, is to help traders estimate their bet being successful or not. Traders estimate the probability of strike price being in ITM by observing delta change through time. Delta is also used as the fundamental to construct hedging strategies. Delta hedging is one way of implied volatility trading to offset directional risk exposure on the underlying asset. Traders expect to earn mean-reverse volatility return from the option bet rather than taking directional bet to trace trend over the market. Straddle is one typical delta hedging strategy. When the market is expected to boost sudden price movement in the near future, traders can use long straddle to profit from increased volatility. The catalyst for rising volatility can come from different aspects. Technical analysts may bet over a spike after a long-playing narrow trading range using long straddle. Fundamental analysts can trade before a regular release of equity financial figures or keen sensation over critical macro eco-political atmosphere evolution. Traders quit to predict the direction of the spike without clear fundamental or supporting indication on a higher chance over one direction. Instead, they may choose to bet on unrealized volatility change given a higher probability certainty than directional bet.

Noting that delta is a cross-sectional static value that it constantly evolves with market development. It indicates the probability to be ITM or OTM at expiration is also changing so that delta hedging is often a dynamic process. It is thus critical to effectively monitor the dynamic evolution of delta change at the same time to as possibly accurately predict implied volatility in delta neutralization strategies. The strategy return will finally be decided by whether traders can as possibly minimize the risk exposure from delta and the difference loss on predicted unrealized volatility compared with actual volatility.

Aforementioned is a basic review on the concept and functional role of delta in option Greeks. We will introduce more in the following series of option learning blogs. Restricted by my own understanding and background as editor, I also welcome comments and discussion over the blog content to learn together. If you are interested in joining our option trading community and learn more about our platform, please check our website at (https://www.tradingflow.com/) or join our discord channel at (http://discord.gg/k4BnGN9wWQ). Happy to take any discussion and progress jointly in option trading!