Vega
Also written ν · Option vega · Kappa
The option Greek that measures sensitivity to volatility — how much an option premium changes for a one per cent change in the implied volatility of the underlying. It is positive for a long call and a long put alike.
In plain language
Four of the five inputs to an option price can be looked up: the spot, the strike, the days remaining and the interest rate. The fifth, volatility, cannot be observed at all. It is an opinion about how much the underlying will move.
Vega is the Greek that prices that opinion. It says how much the premium moves when the market's opinion about volatility moves by one per cent.
And it works the same way for both contract types. Vega is positive for a long call and for a long put. More expected movement raises the chance of finishing deep in the money in either direction, so it raises the value of the right to buy and the right to sell at the same time. This is the one Greek with no bullish or bearish reading at all.
How it works
Vega lives entirely inside the time-value, so it behaves like time value does:
- Largest at the money and for longer-dated contracts, where the outcome is least decided and there is most time for volatility to act.
- Nearly zero at expiry, whatever the strike — there is no time left for volatility to do anything.
The practical use is the one the workbook gives for implied-volatility: when implied volatility is high, traders sell options; when it is low, they buy. A trader taking that view is trading vega, and the workbook's own illustration is a pharmaceutical company awaiting a court verdict, whose implied volatility runs at 70–80 per cent against a historical volatility of about 15 per cent. A buyer at 80 per cent implied volatility can be right about the direction of the verdict and still lose, because volatility collapses the moment the news is out and the vega loss swamps the delta gain.
A note on units. The workbook defines vega as a percentage change in the premium: a vega of 0.80 means the premium changes by 0.80 per cent for every one per cent change in implied volatility. Market systems more commonly quote vega in rupees per one volatility point. Answer in the workbook's terms in the exam; know the other convention exists before you read a broker's terminal.
The formula
Vega = Change in option premium ÷ Change in volatility
On the workbook's percentage convention:
New premium = Old premium × (1 + Vega% × Change in IV in percentage points)
Sign convention:
Long call, long put → vega positive
Short call, short put → vega negative
A worked example
A Nifty call is quoted at Rs 124.50 with a contract size of 50, so one lot costs Rs 6,225. Its vega is 0.80 on the workbook's convention.
Implied volatility rises 5 percentage points — say from 14% to 19% — ahead of a policy announcement, and the index does not move at all.
Premium change = 0.80% × 5 = 4.0%
New premium = 124.50 × 1.04 = Rs 129.48
Per lot = Rs 6,474
Gain = Rs 249 on one lot, Rs 2,490 on ten
Now run the event. The announcement lands, the index is unchanged, and implied volatility falls straight back to 14% — and further, to 12%, because the uncertainty that justified it has gone.
Premium change = 0.80% × (−7) = −5.6%
New premium = 124.50 × 0.944 = Rs 117.53
Per lot = Rs 5,876
Loss from the peak = Rs 598 a lot
The buyer who paid Rs 6,474 at the top of the volatility now holds Rs 5,876 of option, having been exactly right that the index would not fall. He lost Rs 598 a lot to vega alone, before a single rupee of theta is counted.
That is the volatility crush, and it is why the workbook says writers sell into high implied volatility: the premium they collect already has the event priced into it.
Why NISM asks about it
Chapter 16.7 defines vega with the 0.80 illustration used above, and Chapter 16.9 (Implied volatility of an option) supplies the pharmaceutical court-case story that gives vega its meaning. Expect a sign question — vega is positive for both long calls and long puts — and a "which Greek measures volatility sensitivity" identification question.
Common exam traps
- Vega is positive for a long put too. Rising volatility lifts both premiums; it is not a directional signal.
- Vega responds to implied volatility, not to realised moves. The index can be still while vega makes or loses money.
- The workbook quotes vega as a percentage change in premium; most trading systems quote it in rupees per volatility point. Answer in the workbook's terms.
- Vega is largest for longer-dated and at-the-money options and collapses to almost nothing at expiry.
- Do not confuse vega with gamma. Gamma is sensitivity to the underlying's price; vega is sensitivity to its expected movement.
- Vega is not a Greek letter. It is the odd one out in the list, which is exactly why examiners like putting it in a matching question.
Where this is taught
- Series VIII · Chapter 4: Introduction to Optionsintroduced here
- Series V-D · Chapter 16: Introduction to Optionsintroduced here
- Series XVI · Chapter 4: Commodity Optionsintroduced here
- Series IV · Chapter 4: Exchange Traded Interest Rate Optionsintroduced here
- Series I · Chapter 4: Exchange Traded Currency Optionsintroduced here
- Series V-D · Chapter 21: Exchange Traded Interest Rate Options
Related terms
- DeltaThe change in an option's premium for a one-rupee change in the underlying — the first and most used Greek, and the hedge ratio that says how much underlying to hold against an option position.
- GammaThe rate at which an option's delta changes for a one-unit change in the underlying — the second-order Greek, and the reason a delta hedge stops working as soon as the market moves.
- Implied volatilityThe volatility figure that, put into an option pricing model, reproduces the option's actual market price — the market's consensus forecast of how much the underlying will move.
- RhoThe option Greek that measures interest rate sensitivity — the change in an option premium for a one percentage point change in the risk-free rate. It is positive for calls and negative for puts.
- ThetaThe option Greek that measures time decay — the change in an option's premium for a one-day decrease in time to expiry. It is negative for a long option, call or put alike.
- Time valueThe part of an option premium that is not intrinsic value — what the buyer pays for the possibility that the underlying moves further in his favour before expiry. It falls to zero on expiry day.
- Historical volatilityVolatility measured backwards — the standard deviation of the underlying's past percentage price changes, as against implied volatility, which is worked out forwards from the option price.
- Long straddleBuying a call and a put at the same strike and the same expiry — a bet that the underlying moves a long way in either direction, with two break-even points and a maximum loss equal to both premiums.
- Long strangleBuying an out-of-the-money call and an out-of-the-money put with the same expiry but different strikes — the cheaper cousin of the straddle, with a wider band of loss between two break-even points.