How the Options Greeks Vega value is used in Options Trading to calculate the potential effects of volatility?
How Options Greeks Vega value is used in Options Trading to calculate the effects of volatility?
- Thread starter kyliebrow786
- Start date
Basically the Options Greeks are used by Options Traders to have a clearer view of how various elements effect the price of options. Vega for all options is always a positive number because options increase in value when volatility increases and decrease in value when volatility declines.Vega is the value that provides a theoretical sign of the rate at which the price of will change in relation to changes in the volatility of the underlying security. In simple terms, Options Greeks Vega measures the risk of gain or loss resulting from changes in volatility. Here have a look at this article to have a clear understanding of your question. https://steadyoptions.com/articles/options-vega/
Implied volatility cannot be solved from price directly by using a pricing model. There are several algorithmic ways of coming up with IV from a known price. A couple of them are the Newton-Rapson method and method of bisection. Here is a bit of C code that uses Black-Scholes and bisection to find IV:
Code:
#include <cmath>
#include "fin_recipes.h"
double option_price_implied_volatility_call_black_scholes_bisections(const double& S,
const double& K,
const double& r,
const double& time,
const double& option_price){
if (option_price<0.99*(S-K*exp(-time*r))) { // check for arbitrage violations.
return 0.0; // Option price is too low if this happens
};
// simple binomial search for the implied volatility.
// relies on the value of the option increasing in volatility
const double ACCURACY = 1.0e-5; // make this smaller for higher accuracy
const int MAX_ITERATIONS = 100;
const double HIGH_VALUE = 1e10;
const double ERROR = -1e40;
// want to bracket sigma. first find a maximum sigma by finding a sigma
// with a estimated price higher than the actual price.
double sigma_low=1e-5;
double sigma_high=0.3;
double price = option_price_call_black_scholes(S,K,r,sigma_high,time);
while (price < option_price) {
sigma_high = 2.0 * sigma_high; // keep doubling.
price = option_price_call_black_scholes(S,K,r,sigma_high,time);
if (sigma_high>HIGH_VALUE) return ERROR; // panic, something wrong.
};
for (int i=0;i<MAX_ITERATIONS;i++){
double sigma = (sigma_low+sigma_high)*0.5;
price = option_price_call_black_scholes(S,K,r,sigma,time);
double test = (price-option_price);
if (fabs(test)<ACCURACY) { return sigma; };
if (test < 0.0) { sigma_low = sigma; }
else { sigma_high = sigma; }
};
return ERROR;
};
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Robert Morse
Sponsor
I'm not sure how to respond based on how you asked the question. Can you rephrase it? The Vega for each position are representing the change in price for an option for a given change in Vol, all other assumption being the same. Option greeks are tools to monitor, adjust risk or place risk where you want it.
Bob
Bob
Vega is the amount by which the options value changes when the implied volatility moves 1 point.
The total vega of your position is then roughly what your position changes in value when the IV shifts 1 point.
So, option price = 10.- with vega of 0.20. IV goes from 48 to 49: new option price is 10.20
IV goes from 48 to 47: new price is 9.80
Depending on whether it's an ATM or OTM option... the vega changes when the IV changes. For ATM it stays the same... meaning when IV goes from 48 to 24, the price goes from 10 to 5.
Further OTM option's vega drops towards zero when the IV drops, kinda stops working since eventually it falls outside of the probability curve.
If you have a 3k vega position, for instance you have 150 of those ATM options at a total value of 150k, if IV goes up to 49, your position is worth 3k more (153k).
Vega is mainly determined by the underlying spot price and time to maturity. Not so much by the IV itself... that only has a smaller effect on OTM options.
PS, vega for ATM options is easily calculated... it's price / IV.
Again, not for OTM options...
As a rough guide you can say the vega of a 1 sd OTM option is 60-75% of the ATM vega. 2 sd vega is about 25-35% of ATM vega. But this also depends on skew (vol curve across strikes).
The total vega of your position is then roughly what your position changes in value when the IV shifts 1 point.
So, option price = 10.- with vega of 0.20. IV goes from 48 to 49: new option price is 10.20
IV goes from 48 to 47: new price is 9.80
Depending on whether it's an ATM or OTM option... the vega changes when the IV changes. For ATM it stays the same... meaning when IV goes from 48 to 24, the price goes from 10 to 5.
Further OTM option's vega drops towards zero when the IV drops, kinda stops working since eventually it falls outside of the probability curve.
If you have a 3k vega position, for instance you have 150 of those ATM options at a total value of 150k, if IV goes up to 49, your position is worth 3k more (153k).
Vega is mainly determined by the underlying spot price and time to maturity. Not so much by the IV itself... that only has a smaller effect on OTM options.
PS, vega for ATM options is easily calculated... it's price / IV.
Again, not for OTM options...
As a rough guide you can say the vega of a 1 sd OTM option is 60-75% of the ATM vega. 2 sd vega is about 25-35% of ATM vega. But this also depends on skew (vol curve across strikes).
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I have always found it funny with Vega that it measures how much the premium will change when the IV changes, but the IV is actually extracted from the Market Price of the option (using a Black-Scholes type model). So option premium changes because IV changed (but I noticed that IV changed because premium changed)... something circular about it
That's because, contrary to what most believe, IV is an input in the pricing model not an output.
Option market makers use it as a variable input, while all the other inputs are more or less fixed, meaning he can't adjust it... it's a given. So they use their IV (-curve) to get a market accordingly price for the options. IV = input; Price = output.
Retail sees it reversed. They see the price as a given an the IV as an output... but technically it's the other way around.
Remember, options are based on probabilities tied to the underlying price. Those probabilities are based on the (expected) volatility of the underlying.
Well, it's not really true. If you have to price an option in isolation (e.g. on an asset that has no liquid options market), you would use the best guess of the expected volatility as an input. Same goes for other pricing parameters, e.g. if you are pricing a call spread in isolation, you would guess the skew etc.
How do OMMs get their IV curves (or surfaces) in the first place? Do they estimate it based on realized volatility or other isolated modeling?
It depends and is very not straightforward. Most OMMs that you would trade with are closer to HFT stock traders rather than vol traders.
Let's ignore those. Among vol traders (MMs that would keep meaningful positions in gamma or vega overnight), guys making markets in liquid products would usually analyze of the current markets and make adjustments based some richness/cheapness model. Guys who are making a market in something illiquid (where liquidity is low compared to the requested size) would frequently start with realized vol and go from there