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What Is Vomma?
Let me explain vomma directly: it's a second-order Greek measure that shows how the vega of an option changes when market volatility fluctuates. You should know that vomma fits into the group of Greeks—like delta, gamma, and vega—that we use to price options.
Key Takeaways
- Vomma is the rate at which the vega of an option reacts to volatility in the market.
- Vomma is a second-order derivative for an option’s value and demonstrates the convexity of vega.
- Vomma is part of the group of measures—such as delta, gamma, and vega—known as the 'Greeks,' which are used in options pricing.
Understanding Vomma
As a second-order derivative of an option’s value, vomma directly demonstrates the convexity of vega. If vomma is positive, a percentage point increase in volatility leads to a higher option value, which you can see through vega's convexity.
You need to consider vomma and vega together when identifying profitable option trades. They provide details on an option's price and its sensitivity to market changes, influencing how we interpret the Black-Scholes pricing model.
Since vomma is a second-order Greek, it gives insight into how vega shifts with the implied volatility (IV) of the underlying instrument. Calculate a positive vomma, and if volatility rises, vega on your option position increases; if volatility drops, vega decreases. A negative vomma flips this with volatility changes, as shown by vega’s convexity.
In general, if you're holding long options, aim for a high positive vomma; if you're short, look for a negative one.
Here's the formula for vomma: Vomma = ∂ν / ∂σ = ∂²V / ∂σ².
Vega and vomma help gauge the sensitivity of the Black-Scholes model to variables affecting option prices. We consider them alongside the model when making investment decisions.
Vega
Vega lets you understand a derivative option’s sensitivity to volatility from the underlying instrument. It provides the expected change in an option’s price per 1% shift in the underlying's volatility. A positive vega means the option price increases, while a negative vega means it decreases. Building a vega-neutral position can help you mitigate some implied volatility risks.
We measure vega in whole numbers, typically from -20 to 20. Longer time periods lead to higher vega. These values represent multiples for gains and losses—for instance, a vega of 5 on a $100 stock means a $5 loss per point drop in implied volatility and a $5 gain per point increase.
The formula for vega is: ν = S ϕ(d1) √t, with ϕ(d1) = e^(-d1²/2) / √(2π), and d1 = [ln(S/K) + (r + σ²/2)t] / (σ √t), where K is the option strike price, N is the standard normal cumulative distribution function, r is the risk-free interest rate, σ is the volatility of the underlying, S is the price of the underlying, and t is the time to option’s expiry.
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