Vega

Vega is the exposure of an option position to changes in the implied volatility of the
option. Formally, it is defined as the partial derivative of the option value with respect
to the implied volatility of the option. Vega is measured in dollars or other base
currency units. The change in implied volatility is measured in vols (one voló0.01).
Figure 1.17 displays the vega of a typical European call option.
Implied volatility is a measure of the general level of option prices. As the name
suggests, an implied volatility is linked to a particular option valuation model. In the
context of the valuation model on which it is based, an implied volatility has an
interpretation as the market-adjusted or risk neutral estimate of the standard
deviation of returns on the underlying asset over the life of the option. The most
common option valuation model is the Black–Scholes model. This model is now familiar enough that in some over-the-counter markets, dealers quote prices in terms
of the Black–Scholes implied volatility.
Vega risk can be thought of as the ‘own’ price risk of an option position. Since
implied volatility can be used as a measure of option prices and has the interpretation
as the market’s perceived future volatility of returns, option markets can be viewed
as markets for the ‘commodity’ asset price volatility: Exposures to volatility are traded
and volatility price discovery occur in option markets.
Vega risk is unique to portfolios containing options. In her capacity as a pure
market maker in options, an option dealer maintains a book, a portfolio of purchased
and written options, and delta hedges the book. This leaves the dealer with risks
that are unique to options: gamma and vega. The non-linearity of the option payoff
with respect to the underlying price generates gamma risk. The sensitivity of the
option book to the general price of options generates vega risk.

Because implied volatility is defined only in the context of a particular model, an
option pricing model is required to measure vega. Vega is then defined as the partial
derivative of the call or put pricing formula with respect to the implied volatility. 33