What Is Vomma?

Vomma is the rate at which the vega of an option will react to volatility in the market. It is a second-order derivative for an option鈥檚 value. Vomma demonstrates the convexity of vega. A positive value for vomma indicates that a percentage point increase in volatility will result in an increased option value which is demonstrated by vega鈥檚 convexity.

Vomma is part of the group of measures known as the "Greeks" which are used in options pricing. Other measures include delta, gamma, and vega.

Understanding Vomma

Vomma and vega are two factors involved in understanding and identifying profitable option trades. The two work together in providing detail on an option's price and the option price鈥檚 sensitivity to market changes. They can influence the sensitivity and interpretation of the Black-Scholes聽pricing model for option pricing.

Vega

Vega helps an investor to understand a derivative option鈥檚 sensitivity to volatility occurring from the underlying instrument. Vega provides the amount of expected positive or negative change in an option鈥檚 price 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 usually ranging from -20 to 20. Higher time periods result in higher vegas. Vega values signify multiples representing losses and gains. For example, a vega of 5 on Stock A at $100 would indicate a loss of $5 for every point decrease in implied volatility and a gain of $5 for every point increase.

The formula for calculating vega聽is below:

=S(d1)twith(d1)=ed1222andd1=ln(SK)+(r+22)ttwhere:K=option聽strike聽priceN=standard聽normal聽cumulative聽distribution聽functionr=risk聽free聽interest聽rate=volatility聽of聽the聽underlyingS=price聽of聽the聽underlyingt=time聽to聽option鈥檚聽expiry\begin{aligned} &\nu = S \phi (d1) \sqrt{t} \\ &\text{with} \\ &\phi (d1) = \frac {e ^ { -\frac{d1 ^ 2}{2} } }{ \sqrt{2 \pi} } \\ &\text{and} \\ &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{volatility of the underlying} \\ &S=\text{price of the underlying} \\ &t = \text{time to option's expiry} \\ \end{aligned}=S(d1)twith(d1)=2e2d12andd1=tln(KS)+(r+22)twhere:K=option聽strike聽priceN=standard聽normal聽cumulative聽distribution聽functionr=risk聽free聽interest聽rate=volatility聽of聽the聽underlyingS=price聽of聽the聽underlyingt=time聽to聽option鈥檚聽expiry

Vega and Vomma

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

Generally, 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 vomma聽is below:

Vomma==2V2\begin{aligned} \text{Vomma} = \frac{ \partial \nu}{\partial \sigma} = \frac{\partial ^ 2V}{\partial\sigma ^ 2} \end{aligned}Vomma==22V

nba腾讯体育直播ing Vega and Vomma in Options Trading

Vega and vomma are measures that can be used in gauging the sensitivity of the Black-Scholes option pricing model to variables affecting option prices. They are considered along with the Black-Scholes pricing model when making investment decisions.