Definition of vomiting


What is Vomma?

Vomma is the speed at which an option’s vega will react to market volatility. Vomma is part of the group of measures, such as delta, gamma and vega, known as “greeks”, that are used in option pricing.

Key takeaways

  • Vomma is the speed at which an option’s vega will react to market volatility.
  • Vomma is a second-order derivative for the value of an option and shows the convexity of vega.
  • Vomma is part of the group of measures, such as delta, gamma and vega, known as “greeks”, that are used in option pricing.

Understanding Vomma

Vomma is a second-order derivative for the value of an option and shows the convexity of vega. A positive value for vomma indicates that an increase of one percentage point in volatility will result in an increase in the value of the option, which is demonstrated by the convexity of vega.

Vomma and Vega are two factors involved in understanding and identifying profitable option trades. The two work together to provide details about the price of an option and the sensitivity of the option price to market changes. They can influence the sensitivity and interpretation of the Black-Scholes pricing model for option pricing.

Vomma is a second order Greek derivative, which means that its value provides information on how vega will change with the implied volatility (IV) of the underlying instrument. If a positive vomma is calculated and volatility increases, vega in the option position will increase. If volatility falls, positive vomiting would indicate a decrease in Vega. If vomma is negative, the opposite occurs with volatility changes as indicated by the vega convexity.

In general, investors with long options should look for a high, positive value for vomma, while investors with short options should look for a negative one.

The formula for calculating vomiting is as follows:

Vomma

=


ν


σ

=


2

V


σ

2

begin {aligned} text {Vómma} = frac { partial nu} { partial sigma} = frac { partial ^ 2V} { partial sigma ^ 2} end {aligned}

Vomma=σν=σ22V

Vega and vomma are measurements that can be used to measure the sensitivity of the Black-Scholes option pricing model to variables that affect option prices. They are considered in conjunction with the Black-Scholes pricing model when making investment decisions.

Vega

Vega helps an investor understand the sensitivity of a derivative option to volatility that occurs in the underlying instrument. Vega provides the amount of expected positive or negative change in the price of an option per 1% change in the volatility of the underlying instrument. A positive vega indicates an increase in the option price and a negative vega indicates a decrease in the option price.

Vega is measured in whole numbers with values ​​typically ranging from -20 to 20. Higher time periods result in a higher vega. Vega values ​​mean multiples that represent profit and loss. A vega of 5 on Stock A at $ 100, for example, would indicate a loss of $ 5 for each point of decline in implied volatility and a gain of $ 5 for each point of increase.

The formula to calculate vega is as follows:

ν

=

S

ϕ

(

D

1

)

t

with

ϕ

(

D

1

)

=

me


D

1

2

2

2

Pi

Y

D

1

=

l

North

(

S

K

)

+

(

r

+

σ

2

2

)

t

σ

t

where:

K

=

option strike price

North

=

standard normal cumulative distribution function

r

=

risk-free interest rate

σ

=

underlying volatility

S

=

price of the underlying

t

=

time until option expiration

begin {aligned} & nu = S phi (d1) sqrt {t} \ & text {with} \ & phi (d1) = frac {e ^ {- frac {d1 ^ 2 } {2}}} { sqrt {2 pi}} \ & text {y} \ & d1 = frac {ln bigg ( frac {S} {K} bigg) + bigg ( r + frac { sigma ^ 2} {2} bigg) t} { sigma sqrt {t}} \ & textbf {where:} \ & K = text {option strike price } \ & N = text {standard normal cumulative distribution function} \ & r = text {risk-free interest rate} \ & sigma = text {underlying volatility} \ & S = text {price of the underlying} \ & t = text {time until option expiration} \ end {aligned}

ν=Sϕ(D1)twithϕ(D1)=2Pime2D12YD1=σtlNorth(KS)+(r+2σ2)twhere:K=option strike priceNorth=standard normal cumulative distribution functionr=risk-free interest rateσ=underlying volatilityS=price of the underlyingt=time until option expiration

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