# Introduction on Greeks——Delta

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?