Option greeks - Vega

By roma, 16 August, 2020

υ = δV/δσ

V - option price
σ - implied option volatility

The value of the option price also changes when the implied volatility rises or falls. The sensitivity of the option price to changes in volatility is called vega. Vega indicates a potential change in the price of an option if the volatility changes by 1%, all other factors being equal.

For example, if the call option price is $5.58 and its vega is $0.53, then if the implied volatility rises by 1 percentage point, the option price will increase to
$5.58 + $0.53 = $6.11.

However, if the implied volatility falls by one point, the call price will fall to
$5.58 - $0.53 = $5.05.

Buying an option, call or put, involves buying volatility and a long vega position. The owner of the option will earn if the volatility increases and will incur losses if the volatility drops. A trader who has sold options expects the implied volatility to fall as he has a short vega position. Decrease in implied volatility will lead to cheaper option value, and the trader will be able to close the short option position with profit.

Figure 1 shows the relationship between at-the-money call option price and implied volatility. As the volatility increases, the option price increases approximately in a linear proportion.

Fig. 1. Option price
Option price

Mathematically, vega is the first derivative of the option price with respect to volatility. Implied volatility is traded through vega, and options with a long expiry date are generally used for this purpose. Options with a long expiry date have a higher vega, i.e. the value of the vega decreases as the time goes by.

Fig. 2. Option vega
Option vega

 

Delta

Gamma

Theta

Vega

Rho

Long Call

+

+

Pay

+

+

Short Call

Receive

Long Put

+

Pay

+

Short Put

+

Receive

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