###### As an options trader you are exposed to the following risks:

**Delta Risk (**Changes in the underlying asset price*Directional risk*):**Gamma Risk:**Changes in the directional risk of a position**Theta Risk (**The passage of time*Theta/Time Decay*):**Vega Risk (**Changes in implied volatility*Volatility*):

###### So far in the series, we have discussed the Greeks — Delta, Gamma, and Theta. In this article, we will discuss the Greek associated with changes in implied volatility — Vega

###### Let’s dive in!

# The Jumi & Ultraman Scenarios

###### We all know that when volatility increases, the price of an asset tends to begin swinging unpredictably and heavily.

###### Let’s take two option writers — Jumi and Ultraman. Jumi writes some DPX put options and Ultraman writes some DPX call options. In this example, DPX is trading at $10,000, and let’s say that an increase in volatility could cause DPX to begin fluctuating anywhere between $9,000 and $11,000.

## Scenario A

###### When DPX hits $9,000, all put option writers (Jumi & Co) would begin panicking as the put options now have a greater likelihood of expiring in the money.

## Scenario B

###### On the other hand, when DPX hits $11,000, all the call option writers (Ultraman & Co) would begin panicking as the call options now have a greater likelihood of expiring in the money.

## Jumi & Ultraman Conclusion

###### What we can deduce from this is that irrespective of the option (call or put), when volatility increases, the options have a greater chance of expiring in the money.

# The Nifteas Dilemma

###### Now let’s ask ourselves how the scenarios we just discussed above would affect the reasoning of an options trader.

###### Take this scenario:

###### Suppose a trader, we’ll call him “Nifteas”, wants to write some call options with DPX trading at $10,000 and 10 days to expire. There is no intrinsic value here but there is some time value. Assuming the option premium is $420 — ask yourself, if you were in Nifteas’ shoes, would you write the options?

###### Sure, Nifteas could write the options and pocket the $420 premium. Except, what if there is a big FED convention coming up and volatility over the 10 day period is likely to increase, do you think Nifteas would still go ahead and write the option for $420?

###### There’s a chance he won’t because as mentioned earlier, increases in volatility raise the likelihood of options expiring “in the money” so there is a greater chance that Nifteas may lose the whole $420 premium. With that in mind, if all option writers fear volatility, what incentive do they have for even writing options?

## Easy - a higher premium.

###### When volatility increases or is expected to increase, option writers begin to fear that they may write options that could transition to “in the money”.

###### Despite that, if the upside is good enough, this fear becomes obsolete. This is why when volatility is expected to increase, option writers expect higher premiums for writing options, and therefore the premiums of call and put options go up when volatility is expected to increase.

###### Vega is the Greek that helps options traders approximate how much an option price will increase or decrease given an increase or decrease in the level of implied volatility.

# Vega

###### What is Vega?

## Vega measures the risk of changes in implied volatility or the forward-looking expected volatility of the underlying asset price

###### Unlike delta, which measures actual price changes, vega measures changes in expectations for future volatility. Greater volatility makes options more expensive because they have a greater likelihood of hitting the strike price at expiry.

###### Vega tells us approximately how much an option price will increase or decrease given an increase or decrease in the level of implied volatility. While option sellers benefit from a decrease in implied volatility, option buyers do not.

###### It’s key to note that implied volatility reflects price action in the market. When option prices are bid up because there are more buyers, we can expect an increase in implied volatility.

###### Long option traders benefit from prices being bid up, and short option traders benefit from prices being bid down. Due to this, long options have a positive vega value, and short options have a negative vega value.

## Key Points

- Due to changes in implied volatility, the value of vega can fluctuate even without price changes to the underlying asset.
- Vega can increase in reaction to sudden changes in the price of the underlying asset.
- As the option gets closer to the expiration date, the value of vega decreases.

# Option Vega Example

## Vega is expressed as an option’s expected price changes relative to each 1% change in implied volatility.

###### The following table shows how an option’s price is expected to change relative to movements in implied volatility:

###### What we can deduce from this (focusing on the $100 option) is that an option vega of 0.30 represents a $0.30 increase in the option’s price per 1% increase in implied volatility and vice versa. And that with a 3% decrease in implied volatility, the option’s value is expected to be $0.90 lower. **We can do these calculations with the other values as well.**

**We can do these calculations with the other values as well.**

###### In order to estimate an option’s expected price relative to a 1% increase in implied volatility, simply add the option’s vega to its price. For 1% decreases in implied volatility, an option’s price can be estimated by subtracting vega from its price.

# Vega vs. Strike

###### Let’s analyze the following chart to see which options have the most exposure to vega.

## Analysis

- Options that are closest to the underlying asset price (at the money) have the highest vega values.
- An option’s vega is related to the amount of extrinsic value it has because “At the Money” options have the most extrinsic value, and “Out of the Money” options have the least extrinsic value.

# Vega vs. Time to Expiration

###### Let’s take a look at this chart that shows the impact of time to maturity on Vega.

## Analysis

- Options with more time until expiration have larger vega values. Meaning that longer-term options are expected to have more volatile price changes relative to changes in implied volatility. Again, this makes sense because options with a longer time to expiry have more extrinsic value.

###### To understand why options with more extrinsic value have higher vega values, let us consider the following hypothetical scenario:

###### If these option prices both went to $0, implied volatility would be 0%. In order to reach $0, Option B has to lose $0.75 while Option A only has to lose $0.25. Therefore, Option B has a larger vega value.

# Conclusion

- Vega for all options is always a positive number because options increase in value when volatility increases and decrease in value when volatility decreases.
- When position Vegas are generated, however, positive and negative signs appear. When you establish a position selling or buying an option, this will result in either a negative sign (for selling) or positive sign (for buying), and the position Vega will depend on the sum of all the individual Vegas.
- Vega is always the same value for puts as for calls.
- Option prices always increase as the volatility does.
- As vega becomes smaller, volatility has less effect on the option price.
- The size of vega itself mainly depends on the relative value between the underlying asset price and the strike price and on the time to expiry of the option.
- Due to changes in implied volatility, the value of vega can fluctuate even without price changes to the underlying asset.
- Vega can increase in reaction to sudden changes in the price of the underlying asset.
- As the option gets closer to the expiration date, the value of vega decreases.
- Vega is higher on options that have more distant expiration dates.
*However, since those options have higher premiums, the vega is actually higher on options with closer expiration if we look at percentage gain or loss.*

###### That will be all for this article, do not hesitate to reach out to us in the Dopex Discord server for discussions.

# Glossary of terms

**Underlying asset** — The underlying asset, the price of which is being speculated on, for example, Bitcoin.

**Underlying asset**

**Expiry date** — The date the option will expire and be exercised, after this date, the contract is no longer valid.

**Expiry date**

**Strike price** — The price at which the buyer has the right to buy or sell the underlying asset at expiry.

**Strike price**

**Option price (premium)** — The price the buyer pays to the seller for the right to buy or sell the asset at the strike price on the expiry date.

**Option price (premium)**

**In the money (ITM):**

**In the money (ITM):**

- For a call — this term is used when the strike price is lower than the current price of the underlying asset.
- For a put — this term is used when the strike is higher than the current price.

**At the money (ATM):**

**At the money (ATM):**

- For both a call and a put — this term is used when the strike is equal to the current price.

**Out of the money (OTM):**

**Out of the money (OTM):**

- For a call — this term is used when the strike price is higher than the current price of the underlying asset.
- For a put — this term is used when the strike is lower than the current price.

**All options on Dopex are European style, which means they can only be exercised at expiry, unlike American style options that can be exercised any time until expiry**

## About Dopex

###### Dopex is a decentralized options protocol that aims to maximize liquidity, minimize losses for option writers and maximize gains for option buyers — all in a passive manner.

###### Dopex uses option pools to allow anyone to earn a yield passively. Offering value to both option sellers and buyers by ensuring fair and optimized option prices across all strike prices and expiries. This is thanks to our own innovative and state-of-the-art option pricing model that replicates volatility smiles.

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