*Do you use Greeks for evaluating options? If so, do you know that even the slightest differences of the appl**ied methods can influence your trading strategy? In today’s article we will cover the following issues: what the Greeks are used for, who сalculate them and how convenient it is to use them in different terminals.*

Options are one of the most risky and venturous financial instruments. Hypothetically, they allow to win quickly and a lot. The possible loss is clear from the moment of purchase: it is the price you buy the option for, or the option premium. The projected profit, meanwhile, is unlimited. This asymmetry naturally attracts many newcomers to the world of trading, but due to the lack of knowledge and experience they often end up losing. For inexperienced traders, options seem to be a kind of a lottery: the projected loss is known in advance, while the possible profit is supposed to be much higher then the loss. They often neglect the fact that the probability of the loss is, however, disproportionately higher than the probability to win, which leads to losses much more frequently than to victories.

*Greeks on the EXANTE Option Board*

The difference between participating in lotteries and option trading is that with options it is not only the fortune that rules. Option trading is subject to fundamental economic analysis, including the analysis of the underlying market data, which allows professionals to win more often than if they were limited by fortune matters. The methods that can be used for options analysis are rather complicated, but, luckily, today most of calculations can be delegated to the specialized software.

Among the indicators that require complicated calculations which can be delegated to the modern software, there are so-called Greek coefficients, or just the Greeks, to put it simply. They help traders assess their chances to win. The problem is that all trading platforms choose their own way to calculate these indicators, and the reason for that lies not only in the mathematical concepts, but also in the economic fundamentals underlying their essence. This is the rare case when philosophy affects the practical aspects directly, defining the market players’ possibility to win.

EXANTE trading platform developed by the homonymous broker is a relatively young piece of software, but it embodies all strong points of the more mature programs, and offsets most of their weaknesses. Its developers have implemented a non-standard but truly elegant way to calculate the Greeks, thus eliminating a large number of ambiguities that can be found in other trading platforms. Before getting down to proving it through platform comparison, however, it would be sensible to explain what the Greeks are and why traders use them.

**1. What are the Greeks about and why use them?**

The Greek coefficients, or the Greeks, are differential indicators showing the relation between the option price and different market indicators, e.g. the underlying asset price, its volatility, etc. There are first-, second- and third-order Greek coefficients.

The most widely-used Greeks are the first-order ones: Delta (Δ), Vega (ν), Theta (ϴ), Lambda (λ), Rho (ρ), Phi (φ). They are calculated using the existing market data according to the chosen mathematical model, e.g., the Black-Scholes model. They are called Greek, evidently, due to being called after the letters of the Greek alphabet. The only exclusion is Vega, whose Greek-alike name is used along with the Greek letter Nu (ν), while earlier this coefficient was called Kappa.

Second-order Greeks are calculated with the use of the first-order Greeks, third-order Greeks use second-order ones, etc. The most widely-used second-order Greek coefficient is Gamma (Γ).

EXANTE trading platform calculates four Greek coefficients: Delta (Δ), Vega (ν), Theta (ϴ), and Gamma (Γ). Among them, Delta is considered to be the most important for successful trading, so we will dwell on it a little longer.

**1.1 Delta coefficient**

Delta (Δ) is the derivative of the option price with respect to the price of the underlying asset.

The price of the option changes along with the price of the underlying asset. Say, if we trade options on oil, the rise of the oil price by several percent may cause major changes in option prices: some of them may soar, while the others will devalue. Delta reflects the change of the option price caused by the change in the price of the underlying asset by a price unit.

Delta should not be mixed up with the strike derivative of the option price. These values are close to each other, but they are definitely not identical. The strike derivative can be calculated easily as the difference between prices on options with neighboring strikes, while Delta is much more complicated. Sometimes Delta is referred to as the probability of the option execution in the money. This probability is, however, highly idealized: it is calculated assuming a number of propositions, including the one that the price variation is purely accidental. If you decide to calculate the probability of options execution using only Delta, bear in mind that you are likely to lose, while you have not taken into account other important factors — say, political changes which are covered by the conventional news blocks but left aside in mathematical models.

In any case, Delta is useful for traders in at least two cases.

- First of all, it reflects the anticipated dynamics of the underlying asset price. E.g., if the absolute value of Delta is close to 1, the majority of market players are sure that the option will be finished in the money, while Delta close to 0 shows that the option is thought to be finished out of the money. Of course, they can all be wrong, but Delta at least shows the general mood.
- Secondly, Delta by definition shows the change in the option price against the underlying asset price fluctuations. If you know Delta, you can predict the option price dynamics and assess the projected profit from its re-selling.

The option price depends, however, not only on the underlying asset price, but also on time. The price normally goes down as the time to its execution decreases, which is described by another Greek coefficient, Theta.

**1.2 Theta coefficient**

Theta (ϴ) shows how quickly the price of the option falls with each passing day, ceteris paribus.

As we have mentioned before, the option price varies depending on the price of the underlying asset. If the underlying price is constant, the option price usually decreases. This process is called time value decay, and its speed is reflected by Theta. The highest values of Theta are usually reached right before the option expiration, when its price tumbles like an avalanche.

Theta and Delta are useful to estimate the possible value of re-selling the option before the expiration date. If Theta is low, the usual negative trend can be neglected, and at some point the changes of the underlying asset price can lead to the option price increase — the profit in this case can easily be calculated with the help of Delta. If Theta is high, the quick time decay is likely to hinder the profit during the re-sale of the option.

Let’s study a practical case to learn how prices of the underlying asset and of the option correlate with each other. We will take S&P 500 index and analyze a call option with strike price 2,140 expiring July 15, 2016 on it.

*S&P 500 index chart*

*Price of the call option with strike 2,140 and expiration on July 15, 2016*

The fluctuations of the option price correlate with the fluctuations of the underlying index, but the option price swings more severely (the range can be defined by Delta), and its general trend is directed downwards, which is not applicable to the index price (the negative trend is defined by Theta.)

**1.3 Vega coefficient**

Vega (ν) reflects how quickly the option price will change depending on the changes in the underlying asset’s price volatility.

It is another first-order Greek coefficient. Vega is always positive, while the rise of volatility increases the probability to sell the option with a profit. If Vega in EXANTE terminal equals 1, the increase of volatility by one percentage point causes the increase in option price by one price unit. The closer is the execution date, the lower is Vega.

**1.4 Gamma coefficient**

Gamma (Γ) is the derivative of Delta with respect to the price of the underlying asset.

Gamma is a second-order Greek, while it requires a first-order Greek (Delta) to be calculated. If Delta is close to 0 or 1, Gamma will be close to 0. The maximum of Gamma is reached when Delta experiences drastic changes, which indicates higher risks and uncertainty. Gamma is almost equal for call and put options, so in EXANTE interface only one Gamma is shown.

**2. Greeks in EXANTE trading platform. Market analysis example.**

Let’s try to work with the Greek coefficients in EXANTE trading platform. Take an option for S&P 500 index, ticker SPX. Type ‘SPX’ in the search line in the Instruments module and choose Option Board in the context menu after the right click on the instrument’s name.

*The context menu that allows to navigate to the list of available options on a given asset*

You will see the following Option Board:

*S&P 500 index options on the EXANTE Option Board*

These are the options with the nearest expiration date. The screenshot was made on June, 17th, so the expiration date is July, 15th. If necessary. this date can be changed be clicking on 15N2016 and choosing the option from the list. Let’s work with what is chosen by default for now.

This screenshot is not very informative while it does not contain any Greeks. They can be added in the context menu appearing after the click on the icon in the right-upper corner of the table on the Option Board.

*Choosing columns on the EXANTE Option Board*

We have chosen Delta and Theta, and de-activated the Size column.

*EXANTE Option Board with the Greek coefficients (S&P 500 index options)*

**What will Delta and Theta give to us?**

The most evident thing that Delta can show to us is the market mood. Take, for example, a call option with strike price 1,900 and Δ = 0.90. This combination indicates that most traders do not believe that S&P 500 index will go that low in the near future. The same option with strike price 2,160 has Δ = 0.07, which shows that the traders have strong doubt that the index will get higher than 2,160 (later, on July, 15th S&P 500 did strike this height, however.) The buzz is concentrated on the average strike levels, i.e. around strike price 2,060. There Δ = 0.54, and the uncertainty is very high.

The main idea of the Greeks is not to estimate the probability of getting profit on option expiration, but to assess the changes in its price before it finishes. Options allow profiting not only from their settlement, but also from their re-sale prior to the expiration date. Let’s try to assess the chances of it with the help of the Greek coefficients.

Let’s assume that we have bought an option with strike price 2,140 for $5.3. For this option Δ = 0.74, ϴ = –0.27. When we made this screenshot, the index was 2,068. So, there are two ways to get profit from the option we have.

- The index may rise over 2,145 on July, 15. We have already paid $5, on option finishing we will pay $2,140 more and get the sum that equals the new index value.
- Prior to the expiration, the index will definitely rise enough to make the option price higher — at least it will cover the spread and commissions (in our case, these values do not exceed $1.)

Now we know for sure that the first alternative would work: on July, 15 S&P was 2,160, and the deal would give us profit of $2160-$2145=$15. It was not clear on June, 20, however, so let’s try to estimate how profitable the second alternative could be.

As of June, 20 less than a month was left until the option expiration. Let’s assume, there was no Brexit, and we were observing just regular market conditions. What is the projected dynamics of the underlying asset price? You have seen the S&P 500 chart above. For preceding two months, it was hovering around the range of 90 points, while shorter periods allowed a swing of only 40 points. If it had continued, S&P would have grown by at least 20 points by the expiry date. It means the option would have grown by 20*Δ = 20*0.74 = $14.8. This is just a humble estimation: now we know that S&P grew by 90 points by July, 15.

This option seems to be very profitable: it cost only $5, but had a potential to grow dramatically. For the correct analysis, however, we should also take Theta into account. In our case it was rather high: ceteris paribus, this option would lose around a quarter dollar each day in June. If the index had grown by 20 points in four days after the purchase of the option, it would have cost not $14.8, but no more than $13.8, while if it had happened after eight days, the price would not exceed $12. Accordingly, if the index had risen right before the expiration date, there could have been no profit at all.

All things considered, it is often impossible to notionally estimate the profitability of a deal. Real trade requires using strict mathematical methods. The discussion above cannot be called strict, however. Our goal was to show how knowing the Greeks helps improve the projected profit forecast. Now we know that without the Greeks an option trader is literally blind.

**3. Using different trading platforms means having different Greeks?**

If you use Greeks when defining your trading strategy, be aware of two negative factors that can affect it.

First of all, the Greeks always show a forecast, and it is made for the idealized market conditions. Even complicated formulas cannot take into account absolutely all factors that can affect the option price behavior. So, if your calculations show that your position is profitable, it may not really be so. This factor can be related to as system inaccuracy, and it is impossible to get rid of.

Secondly, there are different approaches to the calculation of the Greeks, so they can deviate from what you expect depending on the trading platform you use. A slightest error, in its turn, can turn your calculations upside down, and you will start considering a losing option profitable. This factor can — and should be — demolished by choosing the platform that calculates such important data in the most correct way.

We will examine the difference between Delta and Theta in three trading platforms: EXANTE (our platform), Interactive Brokers and Think or Swim (other popular programs.) To make our study more representative, we will compare the calculated Greeks for three options with absolutely different underlying assets and expiration dates.

To start with, let’s take an option on S&P 500 index with expiration in December, 2018. It is especially important to ensure precise calculations for such long periods. This is how it is displayed in the three programs:

*Options on S&P 500 index with expiration on December 2018 in the Think or Swim trading platform. C in the option name means Call, P stands for Put. The last four digits show the strike price. The Impl column shows the implied volatility of the index.*

*Options on S&P 500 index with expiration on December 2018 in the Interactive Brokers trading platform. The strike price is shown in the center of the table.*

*Options on S&P 500 index with expiration on December 2018 in the EXANTE trading platform. The IV column shows the implied volatility of the index. *

These three screenshots were made within a minute. While the market price changes quickly, several corresponding Bid and Ask cells may show slightly different figures. The Greeks, in their turn, change slowly, so they should apparently be the same on all of the three screenshots. Well, are they? Here are some examples.

Type (C or P) and strike price | Delta in Think or Swim | Delta in Interactive Brokers | Delta in EXANTE | Theta in Think or Swim | Theta in Interactive Brokers | Theta in EXANTE |

P2600 | -0.76 | -0.81 | -0.80 | -0.11 | -0.01 | -0.06 |

P2300 | -0.55 | -0.59 | -0.58 | -0.14 | -0.08 | -0.10 |

P2000 | -0.35 | -0.38 | -0.37 | -0.15 | -0.11 | -0.11 |

P1700 | -0.21 | -0.22 | -0.22 | -0.13 | -0.11 | -0.09 |

P1400 | -0.11 | -0.12 | -0.11 | -0.10 | -0.09 | -0.06 |

C2600 | 0.19 | 0.20 | 0.20 | -0.06 | -0.08 | -0.08 |

C2300 | 0.40 | 0.41 | 0.42 | -0.09 | -0.14 | -0.14 |

C2000 | 0.54 | 0.63 | 0.63 | -0.09 | -0.16 | -0.16 |

C1700 | 0.75 | 0.78 | 0.78 | -0.06 | -0.15 | -0.15 |

C1400 | 0.84 | 0.88 | 0.89 | -0.01 | 0.00 | -0.12 |

We have rounded all figures to the second decimal, like it is done in EXANTE platform. The most significant differences (meaning, when they exceed 1.5 times) are marked with red. Delta in EXANTE and Interactive Brokers programs is almost identical. The figure in Think or Swim is slightly different. The things go worse when it comes to Theta. The coefficients provided by Think or Swim are stand out by dozens percent (sometimes they are even several times higher or lower.) Theta for the last two strikes (P2600 and C1400) is completely different in all of the platforms.

Let’s take other options — options on oil with expiration in September 2016.

*Options on oil with expiration in September 2016 in the Think or Swim platform. C in the option name means Call, P stands for Put. The last four digits show the strike price. The Impl column shows the implied volatility of the index.*

*Options on oil with expiration in September 2016 in the Interactive Brokers trading platform. The strike price is shown in the center of the table.*

*Options on oil with expiration in September 2016 in the EXANTE trading platform. The IV column shows the implied volatility of the index.*

We can compare the figures we get again:

Type (C or P) and strike price | Delta in Think or Swim | Delta in Interactive Brokers | Delta in EXANTE | Theta in Think or Swim | Theta in Interactive Brokers | Theta in EXANTE |

P54 | -0.92 | -0.96 | -0.95 | -0.01 | -0.01 | -0.01 |

P48 | -0.69 | -0.70 | -0.69 | -0.03 | -0.03 | -0.03 |

P42 | -0.22 | -0.22 | -0.22 | -0.03 | -0.03 | -0.02 |

P36 | -0.03 | -0.03 | -0.03 | -0.01 | -0.01 | -0.01 |

C54 | 0.05 | 0.05 | 0.05 | -0.01 | -0.01 | -0.01 |

C48 | 0.31 | 0.30 | 0.31 | -0.03 | -0.03 | -0.03 |

C42 | 0.78 | 0.78 | 0.78 | -0.03 | -0.03 | -0.03 |

C36 | 0.97 | 0.97 | 0.97 | -0.01 | -0.01 | -0.01 |

This time the difference is not that drastic: there are no cases when the deviation exceeds 30%. This may be caused by the shortness of the period till expiration, while the situation has become quite predictable. Well, it may be one of the reasons, but it’s not a very accurate explanation.

The third case we are going to study is an option with the same expiration date (September 2016), but on an absolutely different, exotic underlying asset, VIX, S&P 500 volatility index. It is not oil, a stock or a sum of stocks prices. It is a purely mathematical object that reflects the volatility of prices in the financial market. The higher is the VIX index, the more unstable is the market. In July 2016 it was 11, during Brexit in June it reached 28, while at the end of 2008 it soared to 80. So, the options on this index are a game of predicting how volatile the market will be in the future.

VIX options imply working with second-order uncertainties. VIX illustrates the volatility of the existing assets, which makes its own volatility much higher. Say, it is very unlikely that the price of oil will change by 2 or 3 times during a couple of days, but this is exactly what happened to the VIX index during Brexit. This indicator is too hard to predict even within a month, which hinders, among all other things, correct calculation of the Greeks.

*Options on VIX index with expiration in September 2016 in the Think or Swim platform. C in the option name means Call, P stands for Put. The last four digits show the strike price. The Impl column shows the implied volatility of the index.*

*Options on oil with expiration in September 2016 in the Interactive Brokers trading platform. The strike price is shown in the center of the table.*

*Options on oil with expiration in September 2016 in the EXANTE trading platform. The IV column shows the implied volatility of the index.*

In this case Theta is almost the same in all platforms; the difference can be assigned to the approximation. This cannot be said about Delta, however: it varies much more than in the case with S&P 500 and oil. What is more, at this moment we would like to draw your attention to another column on the option boards, the implied volatility (IV). We will explain this figure in detail in the next part of our overview, but by now you should only know that it indicates the projected future volatility of the underlying asset (in the case of VIX this underlying asset is the whole market!). This indicator is crucial for the calculation of the Greeks. Mistakes in IV inevitably lead to the incorrectly calculated Greeks.

Here is the usual table, but we will take a look not at Delta and Theta as before, but at Delta and IV of the VIX index. In Think or Swim the IV is not calculated for the highest strike prices of put options, so we will only compare the cells where the data is present.

In Interactive Brokers and EXANTE platforms the coefficients are close, while Think or Swim takes the figures for the implied volatility right off the wall. As a result, Delta differs for the most of strike prices, too (not that dramatically for the call options, though.)

Type (C or P) and strike price | Delta in Think or Swim | Delta in Interactive Brokers | Delta in EXANTE | Theta in Think or Swim | Theta in Interactive Brokers | Theta in EXANTE |

P16 | -0.53 | -0.34 | -0.33 | 45% | 73% | 71% |

P14 | -0.26 | -0.17 | -0.17 | 44% | 61% | 64% |

C30 | 0.16 | 0.16 | 0.17 | 128% | 110% | 108% |

C24 | 0.27 | 0.28 | 0.28 | 122% | 100% | 97% |

C20 | 0.39 | 0.42 | 0.42 | 116% | 89% | 85% |

C16 | 0.57 | 0.66 | 0.67 | 115% | 73% | 71% |

C14 | 0.67 | 0.83 | 0.83 | 123% | 61% | 64% |

The conclusion we can make at this point is rather discouraging. Many developers of modern trading software calculate Greek coefficients, but the results of these calculations can evidently differ from each other due to methodological reasons. We know, however, that these data can affect the success of trading, and incorrect Greeks can make you lose. The question is: how to avoid these losses?

There are two possible solutions to this ambiguity.

- The easy solution is to compare indicators in different platforms and believe the ones that were ‘approved’ by the majority. In some cases it may be sensible, e.g. in the case of VIX there is a clear problem of the Think or Swim calculation algorithm, while the other two platforms produce such close figures that they seem consistent. This approach does not work for the SPX call option with strike price 2,600: the Theta is completely different in all three programs, and it is really hard to choose the right one.
- The fundamental solution implies more research: we should first learn how Greeks are calculated, why they may be calculated in different ways, which way is preferable, and where it is implemented. This is the approach that we will describe in the next part. So far, in our view, EXANTE calculates the Greeks in the most reliable way, and we will explain it next time.