Option pricing: intrinsic and time value, volatility and the Greeks
An option premium is intrinsic value plus payment for time and uncertainty. The market expresses uncertainty as implied volatility, and the price’s sensitivity to the market as the Greeks. We cover it all on a real BTC option and the DVOL index.
In lesson 1 we saw BTC call and put prices. Where do those exact numbers come from? The premium has two parts, and its behavior is described by implied volatility and the Greeks. Without them you cannot understand why one exchange is “cheaper” than another.
Intrinsic and time value
- Intrinsic value — what the option would be worth if exercised immediately. Only in-the-money options have it.
- Time value — everything above intrinsic value: payment for the time to expiry and for uncertainty. By expiry it goes to zero.
Example as of October 31, 2026, 06:52 UTC: the 80,000 call is out of the money, so its entire premium of about $3,650 is time value. The 80,000 put is in the money: intrinsic value about $2,715 (80,000 − $77,285), time value about $2,860.
Implied volatility (IV)
Volatility measures how strongly the price moves. Historical volatility is calculated from past moves; implied volatility (IV) is the one “baked into” the current option price — the market’s expectation of future movement. The higher the IV, the more expensive options are, both calls and puts.
Deribit’s DVOL index shows BTC’s 30-day implied volatility as one number, similar to the VIX for stocks. In 2025 BTC DVOL ranged from 32.9 to 71.3 with an average of about 46. In 2026 the high was 90.3 on February 5, when BTC crashed below $60,000; on October 30 the index closed at 40.59. A rough rule: expected daily move ≈ DVOL ÷ √365 — at 40.6 that is about 2.1% a day.
Volatility can spike within minutes. On October 10, 2025, during the crash, BTC DVOL rose from 43 to 64.9 within an hour — about 50% — and almost returned to its previous level two hours later. At such moments quotes on different exchanges update at different speeds.
The Greeks
| Greek | Value | What it means |
|---|---|---|
| Delta | 0.457 | When BTC rises by $1 the call gains about $0.46. The put with the same strike has a delta of -0.543 |
| Gamma | 0.00004 | How much delta changes when the price moves by $1 |
| Theta | −$40.62 a day | The time value the option loses per day — about 1.1% of the premium |
| Vega | $120.05 | How much the option gains when IV rises by 1 point |
| IV | 37.25% | Implied volatility at the mark price |
Why options are compared by IV
An option’s price depends on the quote currency: on Deribit and OKX BTC options are quoted in BTC, on Binance and Bybit in USDT. IV does not depend on currency: it is the same “price of risk”. If one option’s IV is almost the same on two exchanges, a dollar price gap is more often explained by conversion than by a market error. The P2P.Army scanner shows both the price gap and the IV gap (IV spread) side by side — more in lesson 5.
Frequently asked questions
What makes up an option’s price?
Intrinsic value (what the option would be worth if exercised immediately) and time value — payment for the time to expiry and for uncertainty. Time value melts toward expiry.
What is implied volatility?
The volatility “baked into” the current option price — the market’s expectation of how widely the price will move. The higher it is, the more expensive options are.
What is DVOL?
A Deribit index that shows BTC (or ETH) 30-day implied volatility as one number, similar to the VIX. On October 30, 2026, BTC DVOL closed at 40.59.
What do delta, theta and vega show?
Delta — how much the option price changes when the underlying moves by $1; theta — how much the option loses per day; vega — how much it gains when IV rises by 1 point.
Sources
- 1.Options PricingOptions Industry Councilofficial
- 2.Volatility & the GreeksOptions Industry Council
- 3.Deribit launches bitcoin volatility indexThe Block3/31/2021
- 4.Volatility Report: February 2026Block Scholes2/20/2026
- 5.Crypto Derivatives: Analytics Report - Week 42Deribit Insights / Block Scholes10/16/2025
- 6.Inverse OptionsDeribit9/26/2026
About the author
Crypto expert, arbitrage trader and investor
Crypto expert and hands-on crypto arbitrage trader, investor and software developer with over 20 years of experience. On the P2P.Army blog he covers exchange news, P2P and cross-exchange arbitrage.
- Crypto arbitrage
- P2P arbitrage
- Cross-exchange arbitrage
- Crypto exchanges
- Investing
- Software development
