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var CK = ['gclid','fbclid','msclkid','ttclid','twclid'];
var CD = 30;
var AK = UK.concat(CK);function sC(n,v,d){var e=new Date(Date.now()+d*864e5).toUTCString();var c=n+'='+encodeURIComponent(v)+';expires='+e+';path=/;SameSite=Lax';if(location.protocol==='https:')c+=';Secure';document.cookie=c;}
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var fd = {}, has = false;
for (var i = 0; i < AK.length; i++) {
var v = ps.get(AK[i]);
if (v) { fd[AK[i]] = v; has = true; }
}// Click-ID synthesis: when only a click-id is present (no utm_source), derive
// utm_source/utm_medium so downstream analytics groups under the right channel.
var SY = {
gclid: ['google', 'cpc'],
fbclid: ['facebook', 'cpc'],
msclkid: ['bing', 'cpc'],
ttclid: ['tiktok', 'cpc'],
twclid: ['twitter', 'cpc']
};
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for (var sk in SY) {
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// Se ex.first esiste ma e' click-id-only (orphan), completa con i campi nuovi.
// Se ex.first non esiste, usa fd come first.
var newFirst;
if (ex && ex.first) {
var firstHasUtm = false;
for (var i = 0; i < UK.length; i++) if (ex.first[UK[i]]) { firstHasUtm = true; break; }
newFirst = firstHasUtm ? ex.first : mg(ex.first, fd);
} else {
newFirst = fd;
}
sv({first: newFirst, last: newLast});
return;
}var raw = gC(CN);
if (raw) {
try {
var p = JSON.parse(raw);
if (!p.first && hk(p)) sv({first: p, last: p});
} catch(e) {}
return;
}try {
var s = localStorage.getItem(LK);
if (s) { var n = nm(JSON.parse(s)); if (n) sv(n); }
} catch(e) {}
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Understanding how all Greeks are connected to each other helps us not only with evaluating our options but also with risk management. We showed you the 5 main Greeks but in this section we also discuss about second and third order Greeks. In fact we have 3 types of Greeks:
First Order Greeks are not constant and vary as inputs change. (Delta, Vega, Theta, Rho)
Second Order Greeks on the other hand help us understand the exchange rate and acceleration of first order Greeks. (Gamma, Vanna, Vomma, Charm, Veta, Vera)
Third Order Greeks help us understand how second order Greeks change based on the change in first order Greeks. (Speed, Zomma, Color, Ultima)
We can summarize the relationship in the chart below.
Greeks in action 2
First Order Greeks
Delta is important whether we are directional or neutral traders. It helps us understand how the value of our option changes as the price of the underlying changes. This is important because based on the delta, we can calculate our hedge ratio if we want to be delta neutral.
Vega helps the trader understand what his exposure to volatility is. We know that if the value is positive the option increases in value as the volatility increases. If the volatility falls, the value of the option also falls. We also know that the moneyness of an option also affects its vega. If we are very far from at the money, a small increase in volatility will not have a very large impact on the value of the option. Finally, the time to expiration also affects the vega.
Theta is then our time decay. If we are long options, theta plays against us, if we are short options, it plays in our favor. Long dated expiry options have more theta, while the closer we get to expiry the more theta increases.
Rho, is one of the Greeks that matters least to the short-term trader. The change in the risk free rate, the fed fund can affect the value of our option. This is a factor that does not change very quickly as you well know.
Second Order Greeks
Gamma measures the exchange rate of the delta. We already know that long options are long gamma and short options are short gamma. The relationship with the delta is very important especially when we do delta hedging. A delta flat position but with a very high gamma will mean that in reality our position is not flat but will have to be rebalanced even with a small movement of the underlying. This is one of the most important variables for a trader.
Vanna. This Greek helps us understand how the delta changes based on the change in volatility. Vanna is especially important for the delta hedging trader, because it helps manage hedging with changing volatility. While calls have positive Vanna, puts have negative Vanna. This happens because the increase in volatility helps options go in the money.
Vomma. This Greek helps us evaluate the vega change based on the change in volatility. Vomma helps when the volatility change is very high, so it is important to follow the Vomma for long-dated options when there is a high volatility change.
Charm. This helps us measure the delta exchange rate over time. Charm is also known as Delta decay. It is also important to note that the charm depends a lot on the moneyness of the option. OTM calls have a negative charm, the further we move away from the ATM the more the charm is negative and the more the delta value decreases. ITMs have positive charm. OTM puts have a positive charm and this decreases the delta value of the put.
Veta, this Greek helps us to evaluate the Vega exchange rate based on the passage of time. Short-term options have the highest Veta.
Vera shows the exchange rate of the Rho based on the volatility. Again it is not a very important greek for a trader.
Third Order Greeks
Speed. This Greek helps us understand the change of the gamma based on the change of the underlying. So this again is a greek that helps those looking to stay delta and gamma hedged. Since gamma increases as we approach expiration, so does Speed.
Ultima is the Vomma change for the change of the underlying. Ultima helps the trader understand if vomma increases or decreases based on the change in volatility.
Zomma is another interesting Greek, because it helps us understand the change of the gamma in relation to the change in volatility. So when we are long options, we want positive Zomma because we want our gamma to increase with volatility.
Color, this greek helps calculate the gamma change based on the passage of time. So even this Greek can help us understand how the gamma changes during a given period. It helps us if we try to be delta hedged.
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