How to evaluate risks with greeks

By roma, 15 August, 2020

It is very difficult to predict what will happen to the price of an option or a position with several options, because market changes can be unexpected. Since the price of an option does not always change according to the price of the underlying asset, it is important to understand what factors affect the price of the option.

Option traders must understand the following risks in their option positions: delta, gamma, vega and theta. Taken together, these terms are known as Greeks. The Greeks provide a way to measure the sensitivity of an option price to certain factors (asset price, volatility, time). These terms can confuse novice traders and investors, but in fact the Greeks are simple concepts that help to better understand the risk and potential returns of an option position.

 

Calculating option greeks

First, it must be understood that values of Greeks are strictly theoretical. This means that values are predicted on the basis of mathematical models. Most of the information needed to trade options - for example, bid and ask prices, spot prices, trading volume and open interest - is actual data obtained from various exchanges and distributed by your data service provider and/or brokerage firm. Read Option’s greeks - brief description.

But the Greeks must be calculated, and their reliability depends on the model used to calculate them. To calculate the Greeks, you need access to a program that calculates the Greeks in real time. Most brokers provide this information. To trade options professionally, you need to learn math and understand the limitations and benefits of Greeks from a practical perspective

Call

Strike

Put

Price

Delta

Gamma

Vega

Theta

Delta

Gamma

Vega

Theta

Price

 

 

 

 

 

September

 

 

 

 

 

10.01

1.00

0.00

0.00

-0.001

50

0.00

0.00

0.00

0.00

0.007

8.03

0.98

0.01

0.01

-0.004

52

-0.02

0.01

0.01

0.00

0.034

6.13

0.93

0.03

0.02

-0.009

54

-0.07

0.03

0.02

-0.01

0.128

4.37

0.84

0.06

0.04

-0.017

56

-0.16

0.06

0.04

-0.02

0.371

2.87

0.69

0.08

0.06

-0.025

58

-0.31

0.08

0.06

-0.03

0.872

1.72

0.51

0.09

0.07

-0.029

60

-0.49

0.09

0.07

-0.03

1.715

0.92

0.34

0.08

0.06

-0.026

62

-0.66

0.08

0.06

-0.03

2.923

0.45

0.19

0.06

0.05

-0.020

64

-0.81

0.06

0.05

-0.02

4.446

0.19

0.10

0.04

0.03

-0.012

66

-0.90

0.04

0.03

-0.01

6.193

0.07

0.04

0.02

0.02

-0.007

68

-0.96

0.02

0.02

-0.01

8.075

0.03

0.02

0.01

0.01

-0.003

70

-0.98

0.01

0.01

0.00

10.026

 

 

 

 

 

October

 

 

 

 

 

10.08

0.97

0.01

0.02

-0.004

50

-0.03

0.01

0.02

0.00

0.079

8.20

0.93

0.02

0.03

-0.007

52

-0.07

0.02

0.03

-0.01

0.202

6.45

0.86

0.04

0.05

-0.011

54

-0.14

0.04

0.05

-0.01

0.445

4.87

0.77

0.05

0.07

-0.015

56

-0.23

0.05

0.07

-0.02

0.867

3.52

0.65

0.06

0.09

-0.019

58

-0.35

0.06

0.09

-0.02

1.517

2.43

0.52

0.07

0.10

-0.020

60

-0.48

0.07

0.10

-0.02

2.425

1.59

0.39

0.06

0.09

-0.019

62

-0.61

0.06

0.09

-0.02

3.593

1.00

0.28

0.06

0.08

-0.017

64

-0.72

0.06

0.08

-0.02

4.997

0.59

0.19

0.04

0.07

-0.014

66

-0.81

0.04

0.07

-0.01

6.594

0.34

0.12

0.03

0.05

-0.010

68

-0.88

0.03

0.05

-0.01

8.338

0.18

0.07

0.02

0.03

-0.007

70

-0.93

0.02

0.03

-0.01

10.183

 

 

 

 

 

November

 

 

 

 

 

10.21

0.94

0.02

0.04

-0.005

50

-0.06

0.02

0.04

-0.01

0.214

8.43

0.89

0.03

0.06

-0.008

52

-0.11

0.03

0.06

-0.01

0.428

6.78

0.82

0.04

0.08

-0.011

54

-0.18

0.04

0.08

-0.01

0.778

5.30

0.73

0.04

0.10

-0.014

56

-0.27

0.04

0.10

-0.01

1.302

4.03

0.63

0.05

0.11

-0.016

58

-0.37

0.05

0.11

-0.02

2.028

2.97

0.52

0.05

0.12

-0.016

60

-0.48

0.05

0.12

-0.02

2.970

2.12

0.42

0.05

0.12

-0.016

62

-0.58

0.05

0.12

-0.02

4.124

1.47

0.32

0.05

0.11

-0.015

64

-0.68

0.05

0.11

-0.01

5.473

0.99

0.24

0.04

0.09

-0.013

66

-0.76

0.04

0.09

-0.01

6.992

0.65

0.17

0.03

0.08

-0.011

68

-0.83

0.03

0.08

-0.01

8.650

0.41

0.12

0.03

0.06

-0.008

70

-0.88

0.03

0.06

-0.01

10.414

The table above shows options with multiple strikes and expiry dates in September, October and November. The spot price of the stock is $60. The table also shows the Greeks’ delta, gamma, theta and vega values for each option. As the various Greeks are discussed, the reader may return to this table for a better understanding.

The left side of the table shows call options, the right side shows put options. Please note that strike prices are in the middle. Out of the money options - options with strike prices above $60 for calls and with strike prices below $60 for puts. In-the-money call options have a strike price of $60 or lower, and $60 or higher for put options.

The table shows prices and options and their Greeks for multiple expiry dates. Professional traders in hedge funds calculate Greeks in monetary terms (in dollars) in order to assess the potential risks of a position.

To find the monetary value of the Greeks, simply multiply them by the contract multiplier and the price of the underlying asset. The multiplier for most stock option contracts is 100. The size of the Greeks and their possible change depends on
1) the strike price of the option and
2) the expiry time.

 

Change in the price of the underlying asset - delta and gamma

The Delta measures the sensitivity of the option's theoretical value to changes in the price of the underlying asset. The delta is usually presented as a number between -1 and 1, which indicates how much the option price will change when the stock price moves by $1. Alternatively, the delta can also be displayed as a value between -100 and +100.

Thus, the delta from the table shows the actual amount in dollars that the trader will earn or lose if the stock price changes by $1. For example, if the trader has a put option with an expiry date in September and a strike of $64 (i.e. the delta is -0.81), the loss will be $0.81 if the stock price rises by $1. (More details about the delta and its characteristics can be found in the article).

Long call options have a positive delta, while long put options have a negative delta. At-the-money options usually have a delta of about 50 or 0.5. Delta of in-the-money options exceeds the value of 50 in absolute terms, while out of the money options have a low absolute delta (below 50). As the price of the underlying asset changes, the value of the delta will change. When an option is trading very deeply in-the-money (delta is about 100), it will start trading as an equity, i.e. the change in the price of the underlying asset is tantamount to the change in the option price. Meanwhile, the price of a deep OTM option almost does not react to the movement of the stock price. Delta is also very important to consider when building a spreading strategy.

Since delta is an important factor, option traders are also interested in how the delta can change as the stock price moves. The gamma measures the speed at which the delta changes according to the price movements of the underlying asset. Gamma allows you to predict how the delta of an option or the total position will change. Gamma has the highest value for ATM options. Unlike delta, gamma always has a positive value for both long call and long put options. (Read more in this article).

 

Volatility and time - vega and theta

Theta measures how much the option value will decrease over time. For ATM options, the value of theta increases as the expiry date of the option approaches. For ITM and OTM options (both call and put) the value of theta decreases as the expiration date approaches.

Theta is one of the most important concepts for novice option traders. It is necessary to understand the time effect when trading options. The later the expiry time is, the smaller is theta (in absolute terms).

If a trader wants to trade implied volatility, it is best to do so through long-term ATM options that have lower theta than short-term ATM options. If you want to buy an option, it is profitable to buy long-term contracts. If a trader expects low activity in the market in the next week, then it is necessary to sell short-term ATM options, because they have the highest theta and allow you to earn on the sluggish market due to the flow of time.

The last greek, which is considered in this article, is the option vega. Many people confuse vega and volatility. Volatility measures the fluctuations of the underlying asset. Vega measures the sensitivity of an option price to changes in volatility. A change in volatility has the same effect on the value of call and put options. An increase in volatility will increase the price of all options on an asset, while a decrease in volatility will reduce the value of all options.

However, each individual option has its own vega depending on
1) the option's moneyness and
2) the expiry date
and will react to changes in the volatility slightly differently. Since ATM options have the highest vega, these options are more sensible to volatility changes than OTM and ITM options. It should be noted that different strikes can have different implied volatilities, which is called a volatility smile or volatility skew. Vega decreases as time passes, so long-term options have the highest vega.

 

Using greeks to understand combined strategies

In addition to calculating the greeks for individual options, the trader must calculate the total position for each greek for all positions. This will allow you to quantify the various risks of the entire portfolio, including the risk of volatility skew. Since option positions have different risks, and these risks can vary greatly with time and market movements, it is important to be able to correctly assess the risk profile of the portfolio.

 

Conclusions

Greeks help to measure the risk of an option position and determine potential gains/losses. As soon as a novice trader understands the basics of greeks, it is possible to gradually start applying the knowledge gained to practice when implementing option strategies. Unlike investments in stocks, bonds and commodities, it is not enough just to know the delta of an option portfolio when trading options. It is important to be able to determine different risk measurements - gamma, vega, theta, volatility skew.

As financial market conditions are constantly changing, greeks provide traders with the ability to determine how sensitive a particular position is to price fluctuations, changes in volatility and time.

It is 1) the theoretical understanding of the Greeks' mathematics and 2) their influence on the profitability of the position under different conditions on the financial market that will lead a trader to a more professional level of trading.

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