# Relationship between option Greeks

Derivative assets like futures and options have their values derived from the underlying assets. The pricing of options is entirely different from the pricing of stocks. Various factors can affect the price of a call or a put when it comes to pricing them. The underlying price, the option strike price, implied volatility, the time value of the option, and the interest rate are the variables that affect the option premiums.

The Greek alphabets that measure these factors are delta, gamma, vega and theta. Greeks are the support system that helps a trader to gauge and monitor them to assess whether his options positions have to be rebalanced as a result of market fluctuations.

### How do Greeks relate or interact

It's crucial to realise that the Greeks don't operate independently. They are always evolving, and a change in one can have an impact on all the others. Volatility, time and moneyness result in changes in the Greeks.

### Delta

Delta calculates the amount by which the price of an option will fluctuate in response to a change in the stock price. It serves as a gauge of leverage and security. One has to see delta both individually and along with other Greeks.

**Volatility moves delta: **An increase in volatility will make the delta of all options move towards 0.50. An In-The-Money (ITM) option would fall towards 0.50, while an Out-Of-The-Money (OTM) option will rise towards 0.50 as volatility increases. On the other hand, a decrease in volatility will make the delta move away from 0.50. The in-the-money options get closer to 1 and the out-of-the-money option closer to zero as volatility decreases.

**Moneyness affects delta:** As the price of the underlying moves up or down, the options move in and out of money, leading to a change in delta. An At-The-Money (ATM) option has a delta of 0.50. An in-the-money option has delta >0.50, while an out-of-the-money option has a delta <0.50.

The change in delta is measured by gamma. Gamma measures the rate of change of an options delta to a change in the underlying’s price. Gamma is highest for at-the-money options in the short term. While in-the-money and out-of-the-money options have low gamma.

**Expiration:** With more time for an option till expiration, the greater is the uncertainty that it will remain an in-the-money or an out-of-the-money. A delta of 0.50 means the greatest uncertainty. Thus, they tend to move towards 0.50. But as the options approach expiry, delta of in-the-money and out-of-the-money options move away from 0.50, and the uncertainty abates.

It is important to know the relative positions of the other greeks. If a position has a directional bias, one has to monitor other variables like theta, volatility, etc., to know if the trade is on course. If not, one has to take corrective positions or exit. This is true even for non-directional positions.

### Theta

Theta, as we know, is decay in time value and it is favourable for short options and unfavourable for long options. So, if a long option takes a long time for the expected direction of the trade to take place, then the move has to be much larger than the theta lost. Instead, one can take a spread trade to relatively neutralise the theta decay. A spread trade is one where you buy an option and also sell an option of a different strike price of the same type. For example, a call spread involves buying a call at a particular strike and selling a call of a lower strike.

Volatility: An increase in volatility will cause an increase in theta for all options, while a decrease in volatility will cause a decrease in theta for all options. This is because an increase in volatility results in an increase in option prices.

**Expiration:** As the time for expiration approaches, theta for at-the-money options increases while remaining unchanged for in-the-money and out-of-the-money. Ideally, strategies that are theta-centric can be built around at-the-money options to take advantage of higher theta. For example, income strategies like iron fly and credit spreads can be built when the time for expiration is very short.

**Moneyness:** Theta changes as the option moves in and out of the money. Theta decays more as we get closer to the money and decays slower as it gets away from it. At-the-money options have the highest theta decay, while in-the-money and out-of-the-money have lower decay due to theta.

### Vega

Implied volatility is the future volatility expectation in an underlying. Implied volatility is measured by vega. It is important to measure the vega because as volatility goes up and down the option positions follow suit. How much the option position has gone up or down so that corrective action can be followed is what vega tells us. Volatility changes impact the profit and loss of an option position, and so these need to be monitored closely.

Time: Short-term options have lower vega value than their long-term counterparts. A vega of a weekly option with the same strike price will have a lower value than a vega of a monthly option of the same strike price. As the time to expiration nears, vega reduces. Implied volatility is more in the short-term options and less in the long-term options. So, despite a smaller vega value in the short-term options, vega is affected as implied volatility changes much more in the short term.

**Volatility: **An increase in volatility leads to an increase in vega and a decrease in volatility leads to a decrease in vega.

**Moneyness:** At-the-money options have the maximum vega, while in-the-money and out-of-the-money options have low vega.

It is important to understand the impact of implied volatility as there can be situations when options are held in anticipation of a move; here, even though the underlying moves, the option doesn’t. This is because of implied volatility that has already been built in.

Many a time, uninformed traders during earnings seasons take directional bets and buy calls or puts based on the expected results without looking into the built-in implied volatility in the options. The result is the underlying moves, but the options fall as implied volatility cools off with the earnings playing out.

Therefore, one needs to employ the right strategy for such events. This includes taking a spread trade in case of a directional bias or employing an iron condor or a strangle as the implied volatility reaches a higher percentile before the event.

It helps in doing a little bit of volatility analysis before taking a directional trade or a non-directional trade. As a thumb rule, it is good to buy options when volatility is low and sell options when it is high.

### Conclusion

Options trading without understanding Greeks and their interactions can burn a hole in the pocket unless you are abundantly blessed by lady luck. Each factor can change the risk profile of a trade. Greeks measure the sensitivity of these factors to the option price and knowing these can immensely help one become a better trader.

### Things to remember

- The pricing of options is entirely different from the pricing of stocks.
- The underlying price, the option strike price, implied volatility, the time value of the option, and the interest rate are the variables that affect the option premiums.
- The Greek alphabets that measure these factors are delta, gamma, vega and theta.
- Undertaking volatility analysis before taking a directional trade or a non-directional trade helps. The thumb rule says it is good to buy options when volatility is low and sell options when it is high.