Option Vega

Option vega is the estimated change in an option's price, per share, for a one-percentage-point change in implied volatility, with the stock price, time to expiration and other inputs held constant. FINRA defines it as "the rate of change in an option's theoretical value in response to a one-point change in implied volatility," and the Options Industry Council says that vega "measures an option's sensitivity to changes in implied volatility." Implied volatility is the level of future movement the market price of an option implies; vega measures how much that price responds when the level changes. The council's glossary also lists kappa with the identical definition and cross-refers the two entries.

What one point means. The council describes vega as the change in premium "based on a 1% (100 basis points) change in the implied volatility assumption." That 1% is one percentage point of volatility, as FINRA's "one-point change" makes clear: a move from 25% to 26%, not a 1% increase in the 25% itself, which would take it only to 25.25%.

The sign. Higher implied volatility means the market expects bigger moves, and a bigger expected move in either direction makes an option more valuable to its owner. The council's strategy pages say so for both kinds of bought option: on buying a call or a put, "an increase in implied volatility would have a positive impact on this strategy," because "volatility tends to boost the value of any long option strategy." Bought calls and bought puts therefore both carry positive vega. Its pages on writing uncovered calls and puts state the reverse, that an increase "would have a negative impact on this strategy," so sold options carry negative vega.

Where vega is largest. The council notes that "longer-term options tend to have higher Vega than near-term options," and that in-the-money and out-of-the-money options "have lower Vega" than at-the-money ones. A long-dated option at the money is therefore the most exposed to a change in implied volatility, and a short-dated, deep in-the-money or far out-of-the-money option the least.

Price moves with no move in the stock. The council points out that "Vega and implied volatility can change without any movement in the underlying," and that implied volatility "tends to increase when there is uncertainty or anticipated news, while it tends to decrease in times of calm." So an option can lose value after a scheduled announcement, such as an earnings report, even when the stock moves the expected way, if implied volatility falls by more than the move adds. The council's own judgment is that changes in implied volatility can have "drastic effects on an option price, probably second only to underlying price in importance."

Vega is quoted per share, for a one-point change in implied volatility. Multiply it by the change in implied volatility, in points, and then by the number of shares the contracts cover.

An example of how it works, with illustrative figures: a stock trades at $210, and a call with a $210 strike and 90 days to expiration is quoted at $11.40 with implied volatility of 25% and a vega of 0.41.

• If implied volatility rises 3 points to 28% and nothing else changes, the call should gain about 3 × 0.41 = $1.23 a share, to about $12.63, or $123 on one 100-share contract.
• If implied volatility falls 5 points to 20%, the call should lose about 5 × 0.41 = $2.05 a share, to about $9.35, or $205 a contract.
• A call at the same strike with only two weeks to run might have a vega of about 0.16, so the same 3-point rise would add only about $0.48 a share.
• Someone who sold the 90-day call has a vega of −0.41 on it, so the 3-point rise costs the writer about $123 a contract.

These are estimates. Vega itself changes as the stock moves, as time passes and as implied volatility changes, and a move in implied volatility usually arrives together with a move in the stock.

Pros

• Explains why an option's price can change on a day the stock does not move.
• Puts a dollar figure on exposure to a change in implied volatility, which is otherwise easy to overlook.
• Shows why longer-dated options react more to shifts in market expectations than short-dated ones.

Cons

• Implied volatility is itself an output of a pricing model, so vega is an estimate built on another estimate.
• It assumes the stock price and time stay fixed, and implied volatility rarely changes alone.
• Implied volatility differs across strikes and expirations of the same stock, so one contract's vega does not describe the others.
• A buyer can be right about the direction of the stock and still lose money if implied volatility falls far enough.