U - Z

Vanna

Variance measures the degree of variability of a variable.

Commonly referred to within linear algebra, a vector is a quantity which possesses a size and direction. Opposed to a scalar quantity, which only possesses size, vectors can be anything from the movement of a car, to temperature.

In finance, a vector can describe stock price movements or option price changes, and a host of applications can be derived from vectors and matrices.

Vega

The greek letter Vega is commonly used to denote variables within a range of contexts. In the case of quantitative finance and option pricing, vega is an important concept in assessing the risks of a derivative. We know that financial derivatives are highly dependent on the volatility of the underlying asset, but how do we measure the effect of volatility on the option?

This is where vega comes in. It measures the sensitivity of the option price to the volatility of the underlying. By considering the Taylor expansion,

We can see that vega is seen as the 5th term along the expansion given above.

To illustrate the use of vega to assess risk, consider the case of a European option. Because the vega is the same for both calls and puts, we can show that with a substantial time to maturity remaining, the option value is highly sensitive to changes in volatility.

The vega is essentially the dollar change in the option value assuming a 1% change in the volatility of the underlying. For example, if the option value was $4.50 and the vega was 25, it can be said that a 1% increase in the underlying volatility will shift the option value to $4.75.

Carrying on from the definition of vega, we look at another hedging parameter; the volga. This gives us an even greater sensitivity assessment by showing the sensitivity in vega with respects to the option price.

The vega is the change in option value with respects to the change in volatility of the underlying:

Consequently, the option vega is the 2nd derivative of the option value with respects to the change in volatility:

Which can be considered as "gamma-vega" of the option, but is more commonly just considered as volga or vomma.

Please see Volga

Wave Function

Please see Brownian Motion