Over the course of the last few chapters, we talked in detail about each of the five option Greeks. We saw how each of these Greeks affect the price of an option. Given how extensive the last few chapters were, it is time to summarize Option Greeks including talking about how Greeks interact with each other. In this chapter, we will combine the various Greeks that we have studied over the past few chapters to understand how Greeks interact with each other. Kindly note that we won’t be learning anything new that we haven’t already studied over the last few chapters. Just that we will be highlighting some of the key properties of Greeks for ease of reference. That said, before summarizing our discussion on Greek interaction, let us first recap the basics of Greeks.
Recapping Greeks
We know that there are broadly seven factors that impact the price of an option. These factors are as mentioned below:
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Type of option (Call vs. Put)
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Underlying price
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Strike price
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Volatility
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Time to expiration
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Interest rate
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Dividend
Of these seven factors, we had seen that two remains constant - type of option and strike price. Each of the other factors keep changing. Some keep changing every moment, such as underlying price, volatility, and time to expiration; while others change infrequently, such as interest rate and dividend.
How these factors impact the price of an option can be roughly estimated using option Greeks. Over the past few chapters, we saw that there are five option Greeks: Delta, Gamma, Vega, Theta, and Rho. Let us again highlight what each of these Greeks represent:
| Greek | Meaning |
| Delta |
Delta measures the rate of change in the price of an option for a 1 point change in the price of the underlying asset.
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| Gamma |
Gamma measures the rate of change in Delta for a 1 point change in the price of the underlying asset.
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| Vega |
Vega measures the change in option price for a 1 percent change in Implied Volatility (IV).
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| Theta |
Theta measures the change in option price for a one unit change (usually 1 day) in the time left to expiration of an option.
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| Rho |
Rho measures the change in option price for a 1 percent change in the risk- free interest rate.
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In the last few chapters, we also saw that the kind of impact Greeks have on option prices depends on the type of option (call or put) and the type of position (long or short). Let us now highlight this below:
| Greek | Long Call | Short Call | Long Put | Short Put |
| Delta | Positive | Negative | Negative | Positive |
| Gamma | Positive | Negative | Positive | Negative |
| Vega | Positive | Negative | Positive | Negative |
| Theta | Negative | Positive | Negative | Positive |
| Rho | Positive | Negative | Negative | Positive |
In the above table, positive means the respective Greek is expressed as a positive number for the said option position, while negative means the respective Greek is expressed as a negative number for the said option position. For instance, for a short call, Vega is expressed as a negative number; while for a long call, it is expressed as a positive number.
Finally, let us conclude our recap section on Greeks by talking about some examples:
Delta
| Delta (Call) | 0.6 | Delta (Call) | 0.6 | |
| Call Premium | ₹4 | Call Premium | ₹4 | |
| Delta (Put) | -0.4 | Delta (Put) | -0.4 | |
| Put Premium | ₹2.5 | Put Premium | ₹2.5 | |
| Change in Underlying Price | +₹5 | Change in Underlying Price | -₹4 | |
| New Call Premium | ₹7.0 | New Call Premium | ₹1.6 | |
| New Put Premium | ₹0.5 | New Put Premium | ₹4.1 |
In the above table, change in the underlying price is multiplied with the Delta. The figure that is arrived is then added to the option premium to arrive at the new option premium.
Gamma
| Delta (Call) | 0.6 | Delta (Call) | 0.6 | |
| Gamma (Call) | 0.03 | Gamma (Call) | 0.03 | |
| Delta (Put) | -0.4 | Delta (Put) | -0.4 | |
| Gamma (Put) | 0.03 | Gamma (Put) | 0.03 | |
| Change in Underlying Price | +₹5 | Change in Underlying Price | -₹4 | |
| New Delta (Call) | 0.75 | New Delta (Call) | 0.48 | |
| New Delta (Put) | -0.25 | New Delta (Put) | -0.52 |
In the above table, change in the underlying price is multiplied with the Gamma. The figure that is arrived is then added to the Delta to arrive at the new Delta.
Vega
| Vega (Call) | 0.15 | Vega (Call) | 0.15 | |
| Call Premium | ₹4 | Call Premium | ₹4 | |
| Vega (Put) | 0.15 | Vega (Put) | 0.15 | |
| Put Premium | ₹2.5 | Put Premium | ₹2.5 | |
| Change in Implied Volatility | +5% | Change in Implied Volatility | -6% | |
| New Call Premium | ₹4.75 | New Call Premium | ₹3.10 | |
| New Put Premium | ₹3.25 | New Put Premium | ₹1.60 |
In the above table, change in implied volatility is multiplied with Vega. The figure that is arrived is then added to the option premium to arrive at the new option premium.
Rho
| Rho (Call) | 0.05 | Rho (Call) | 0.05 | |
| Call Premium | ₹4 | Call Premium | ₹4 | |
| Rho (Put) | -0.05 | Rho (Put) | -0.05 | |
| Put Premium | ₹2.5 | Put Premium | ₹2.5 | |
| Change in Interest Rate | +1% | Change in Interest Rate | -1% | |
| New Call Premium | ₹4.05 | New Call Premium | ₹3.95 | |
| New Put Premium | ₹2.45 | New Put Premium | ₹2.55 |
In the above table, change in interest rate is multiplied with Rho. The figure that is arrived is then added to the option premium to arrive at the new option premium.
Conclusion
In the next module, which will be on Option Strategies, we will continue our discussion on Option Greeks. There, using various examples, we will see how Greeks can impact each of the strategies, right from basic strategies to complex ones. For now, we would advise the reader to get a good hang of Option Greeks. If need be, quickly go through each of the previous five chapters to get a firm grip on each of the Greek. The objective is to understand how these sensitivities respond to changing market conditions, so as to better manage the risk(s) involved in a trade setup. Let us now conclude this chapter by talking about some of the key things that we learned about Greeks in the preceding five chapters:
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Option Greeks affect only the time value component of the option price and not the intrinsic value component.
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Option Greeks are dynamic, meaning that they keep changing every moment as and when incoming information comes in.
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Delta is highest for options that are deep ITM and lowest for options that are deep OTM. For options that are ATM or NTM, absolute Delta is approximately 0.5.
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The higher the absolute Delta, the more responsive is the option price for a given change in the underlying price, and vice versa.
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Delta is also expressed as the probability of an option expiring ITM. For instance, an absolute Delta of 0.70 means that there is a 70% probability of the option expiring ITM.
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IVs and absolute Delta of an ITM option are inversely correlated, meaning a rise in IVs tends to reduce Delta of an ITM option, and vice versa.
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IVs and absolute Delta of an OTM option are directly correlated, meaning a rise in IVs tends to increase Delta of an OTM option, and vice versa.
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As absolute Delta approaches an extreme (0 or 1), its slope gets smaller and smaller before eventually approaching 0.
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The slope of the Delta (i.e. Gamma) tends to be at its highest when the underlying price is at or near the strike price.
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When the underlying price starts moving away from the strike price, Gamma starts reducing. When an option is deep ITM or deep OTM, the Gamma of that option approaches zero.
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The higher the Gamma, the greater is the change in Delta for a given change in the underlying price, and vice versa.
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Gamma is an option seller’s enemy. Pay careful attention to Gammaif short an option, especially an ATM option as Gamma for ATM options tends to get steeper as the expiry approaches.
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Calls and Puts having the same strike price and expiration date have the same Gamma. For instance, Nifty 12000 CE and 12000 PE expiring on February 27th would have the same Gamma.
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ATM options with low IVs tend to have the highest Gamma. Generally, as IVs increase, Gamma reduces, and vice versa. The only exception to this is when options are deep ITM or deep OTM.
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For options that are deep ITM or deep OTM, given that they have absolute Deltas at an extreme, as IVs increase, so does the Gamma, and vice versa.
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Theta is an option holder’s enemy. As Theta erodes the time value component of an option with each passing day, option holders must pay careful attention to this vital option Greek.
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As ATM options have the highest time value, Theta tends to be maximum for ATM options and starts to reduce as the options move away from being ATM.
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Absolute Theta of an ATM option increases rapidly in the last few days of expiry. This causes the time value, and subsequently the option premium, to rapidly lose value towards expiry.
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ITM options have more of intrinsic value and less of time value. Because they have less time value, they tend to have lower Theta and as such, are not as much impacted by time decay.
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The deeper an option is ITM, the lesser would be the impact of Theta on the price of such options. This is because deep ITM options have Theta that is nearly zero.
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OTM options have only time value.However, as they have less time value than ATM options, Theta does not have as much impact on OTM options as it does on ATM option.
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IVs and Theta are directly correlated. The higher the IVs, the higher would be the time value of an option and hence the higher would be the Theta, and vice versa.
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The higher the time to expiration, the higher would be the Vega. As the time to expiration reduces, so does the Vega, meaning that the impact of IVs on option price will also start reducing.
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Vega tends to be highest for ATM options and starts reducing as the option moves away from being ATM. Deep ITM and deep OTM options have very low Vega.
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Because ATM options have the highest Vega, the greatest impact of changes in IVs tends to occur on options that are ATM or NTM.
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Rising volatility works against an option seller and can rise sharply in a quick span of time. As a result, short exposure to Vega always needs to be carefully monitored.
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Calls and Puts having the same strike price and expiration date have the same Vega. What can differ however is the IVs.
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A surge in interest rates benefits call options and hurts put options, and vice versa. However, given that interest rates don’t change every day, the impact of Rho on option prices is limited.
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Deep ITM options have high absolute Rho, while deep OTM options have low absolute Rho.
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Comments & Discussions in
FYERS Community
ravi kiran commented on February 19th, 2020 at 10:40 PM
excellent, simple in language and to the point, thank you.
please also tell where to find these data of the greek values on a daily basis.
Shriram commented on February 20th, 2020 at 11:02 AM
Thank you Ravi! You could find these values using an Option Price Calculator
Bidyut Chakraborty commented on August 31st, 2020 at 2:58 PM
On the day of expiration, NSE dont show IV (implied volatility) in the Option chain table. Can we somehow compute them through Black Scholes method?