Implied volatility (IV)

From price to volatility

An option's model price depends on five things: the underlying's price, the strike, the time to expiry, the interest rate, and how much the underlying is expected to move, its volatility. The first four are known. So instead of asking the model for a price, the market works backwards: given the price options actually trade at, what volatility would make the model agree? That number is the implied volatility.

IV is therefore not a forecast someone publishes; it is a way of quoting option prices. For a given strike and expiry, a higher IV means a more expensive option; what IV adds is a common scale across strikes and expiries, which raw prices don't share. That makes IV the common unit traders use to compare options with each other, across strikes, expiries and venues.

Reading the number

IV is quoted per year. To turn it into an expected move over a shorter period, scale it by the square root of time:

• With BTC at $100,000 and an IV of 50%, a one-standard-deviation move over 30 days is 50% × √(30/365) ≈ 14.3%, about $14,300 either way.
• Over one day it is 50% / √365 ≈ 2.6%, about $2,600.
• An at-the-money straddle (a call plus a put) costs roughly 0.8 × that 30-day move: about $11,400. The Black-Scholes price of the 30-day straddle at 50% is $11,428.

A one-standard-deviation move covers roughly two days out of three; the rest of the time the move is bigger. Crypto returns have fatter tails than the model assumes, so large moves come more often than that rule suggests.

One option, one IV

Every option has its own IV, and they are not all equal. Out-of-the-money puts usually trade at higher IV than at-the-money options (the market pays up for crash protection), and short-dated IV jumps around events while long-dated IV moves slowly. The pattern across strikes is the smile or skew; the pattern across expiries is the term structure. Both are on the BOSS Dashboard.

Because of that, a single "IV of bitcoin" needs a definition. BOSS uses:

• ATM IV: the average of the at-the-money call's and put's IV at an expiry;
• ATM IV 7d / 30d: that number interpolated across the listed expiries to a fixed 7- or 30-day horizon, so it can be compared over time and against realized volatility measured over the same window;
• structure IV: on a strategy page, the average IV of the legs it is built from.

What moves IV

IV rises when the market expects bigger moves or wants protection: ahead of an FOMC decision or a CPI release, around an ETF decision, and above all during a sharp sell-off. It tends to drift down in quiet markets. After a scheduled event, IV usually drops back whatever the price did, the "volatility crush".

What an option position gains or loses from a change in IV is its vega. Whether options are expensive or cheap is a comparison between IV and the volatility the market then actually delivers.

Where the numbers come from

Each venue computes and publishes an IV with every option quote, from its own mark price. BOSS uses those values as they arrive, so the same option can show a slightly different IV on Deribit, OKX and Bybit: the venues' prices differ, and so do their forwards.