Vega explained: what a volatility point is worth

An option's price moves with the coin's price, the time left and implied volatility. Vega is the part that answers to volatility: what the option gains, in money, for each point it rises. The site's options pages compare everything in volatility, and vega is how a gap measured in points becomes dollars, which is how Options priced apart values one against Bybit's.

What is vega?

Vega is how much an option's price changes for one point of implied volatility (implied volatility explained), with the coin's price and the time left held still. In the table below, the option at the money a month out has a vega of $91.26: at 51% volatility it's worth about $91.26 more than at 50%.

A call and a put on the same strike and expiry have the same vega, and it's always above zero for whoever holds the option: more volatility, more chance of a big move. The site works it out with Black's model, the one the exchanges price with, from the forward, the price set now for the coin at expiry, so it comes out in dollars for an option on one coin.

Why is vega largest at the money?

Far out of the money, an option pays only after a big move, and a point more volatility barely changes that small chance. Far in the money, it moves almost one for one with the coin, and volatility hardly touches it. At the money, all it's worth is the chance of a move, so each point counts for most.

So across one expiry's strikes, vega is a hump with its top at the money, leaning a little towards the higher strikes, as the model has prices move in proportion. Each strike has a volatility of its own (the volatility smile); vega says what a point of it is worth there.

Why does vega grow with time to expiry?

Volatility is a rate a year, and the move it implies grows with the square root of the time left: four times as long, twice the move. Vega at the money grows the same way. In the table, an option 90 days out has about 3.6 times the vega of one 7 days out, close to the square root of 90 ÷ 7.

The hump widens, too. A week out, a strike a fifth from the forward has almost no vega; a quarter out, it keeps well over half the vega at the money. So the dated options furthest out are the most sensitive to volatility, at the money and away from it.

Vega in dollars, for one coin

With example inputs, a forward of 80,000 and a volatility of 50% at every strike, Black's model, the formula in the site's own code, gives vega a point in dollars for one coin:

Example figures, not market data.

Down a column, vega peaks at the money. Across a row, it grows with time, fastest away from the money. At the money there's a rule of thumb: vega a point is about 0.4 × the forward × the square root of the years left ÷ 100. For the table's month, that's about $92, against $91.26 from the full formula.

How does a gap in volatility become dollars?

Where two exchanges price one option at different volatilities, the points between them times its vega are roughly what the gap is worth, in dollars a coin.

That's how Options priced apart values a gap against Bybit. Bybit's options are struck, priced and settled in tether on its own index (coin-settled vs tether options), so their prices can't be set against Deribit by Coinbase's and OKX's, which are in the coin; their volatility can. Where one exchange's bid volatility is above another's ask, the site multiplies the points apart, to a tenth, by vega at the volatility you'd buy at, from that exchange's forward, the strike and the time to expiry, and writes the result "≈ $".

Why only roughly?

Vega is the slope of the option's price at one moment.

It moves. Time shrinks it, as the table reads from right to left: the month's $91.26 at the money is $44.17 by the last week, if nothing else changes. A move in the coin's price shifts the strike away from the money or towards it, and away from the money, vega moves with volatility too.

A big gap isn't a straight line. An option's price curves as its volatility climbs, most away from the money and near expiry, and there vega times the points falls short. Ten points on the table's options, from 50% to 60%:

Example figures, not market data.

Near the money, a gap of a point or so comes out within cents.

It isn't locked in. Bybit's option settles in tether on its own index, so the two legs don't cancel out at expiry. The dollars are roughly what you'd make if the two volatilities met and you closed both, with tether at a dollar, less each exchange's standard taker rate on both legs.

Where to find it

• On Bitcoin's and Ethereum's pages, the chain writes every bid and ask as implied volatility, and Options by expiry gives the Gap at the money in points: times vega, that's dollars a coin.
• Options priced apart, under the chain (Bitcoin's): open See every one, then Against Bybit, in tether. Apart, a coin is "≈ $" with the points under it, and After fees is "≈ $" with if tether holds under it.
• The Options trade simulator (Bitcoin's) gives the volatility you'd trade at, after walking each exchange's book.
• The futures and options index has every coin's volatility at the money, and the scoreboard each exchange's spread at the money, in points too.

More in implied volatility explained and crypto options arbitrage.

Not financial advice. Prices move while you read them.