Volatility and pricing

Implied volatility, the relationships that tie option prices together, and how crypto venues price them.

1. Implied volatility (IV)

   Implied volatility is the volatility of the underlying that, plugged into an option pricing model, reproduces an option's market price: the market's price for expected movement, which includes a risk premium, quoted as an annualized percentage.

2. Realized volatility (RV)

   Realized volatility is how much the underlying actually moved over a past window, measured as the standard deviation of its daily log returns and annualized, so it can be compared directly with implied volatility.

3. Implied vs. realized volatility

   Comparing implied with realized volatility asks whether options are priced for more movement than the underlying is delivering; IV usually sits above RV, and that gap, the volatility risk premium, is what option sellers try to collect.

4. Volatility smile

   The volatility smile is the shape implied volatility takes across strikes for a single expiry: usually lowest near the money and higher in the wings, and in crypto tilted toward whichever side the market is paying up for: usually the puts in sell-offs and bear phases, often the calls in strong rallies.

5. Volatility skew and risk reversal

   Volatility skew is how implied volatility tilts across an expiry's strikes, measured at 25 delta: put skew is 25-delta put IV minus at-the-money IV, and the risk reversal, 25-delta call IV minus 25-delta put IV, sums up the tilt between the wings in one signed number.

6. Term structure of volatility

   The term structure of volatility is at-the-money implied volatility plotted against time to expiry; it normally slopes upward (contango), and it inverts (backwardation) when the market expects turbulence in the near term.

7. Volatility surface

   The volatility surface is implied volatility across both strike and expiry at once, the smile of every expiry laid along the term structure; traders usually read it by delta rather than by strike, so expiries compare on equal terms.

8. DVOL (Deribit Volatility Index)

   DVOL is Deribit's implied volatility index for bitcoin and ether: a 30-day expected volatility computed from the prices of Deribit's own options across a wide range of strikes, with a methodology modeled on the VIX, quoted as an annualized percentage.

9. Put-call parity

   Put-call parity is the no-arbitrage relationship between a European call and put with the same strike and expiry: the call's price minus the put's price equals the forward price minus the strike (discounted to today).

10. Box spread

    A box spread combines a bull call spread and a bear put spread on the same two strikes and expiry, so it pays exactly the strike width at expiry whatever the underlying does; its price today therefore implies an interest rate.

11. Forward price and basis

    The forward price is the price agreed today for buying the underlying at a given expiry; the basis is how far it sits above or below spot, forward / spot − 1, and its annualized value is the market's carry for that horizon.

12. Index price and mark price

    The index price is a venue's reference spot price, computed from several spot exchanges; the mark price is the venue's own fair value for an instrument, used for margin and liquidation, which is neither a bid, an ask nor a guaranteed fill.

13. Black-Scholes and Black-76

    Black-Scholes is the classic model that prices a European option from the underlying's price, the strike, time, the interest rate and volatility; Black-76 is its version written on the forward, which is how crypto options are priced.

14. Probability of profit (PoP)

    Probability of profit is the estimated chance that a strategy ends with a gain at expiry, after its entry costs; BOSS computes it from a lognormal distribution around the expiry's forward at the at-the-money implied volatility.

15. Inverse vs linear options

    Inverse options are quoted, margined and settled in the coin itself, like the coin-margined BTC and ETH options BOSS follows on Deribit and OKX; linear options are quoted and settled in a stablecoin, like the ones BOSS follows on Bybit, so their payoff in dollars is the textbook one.

16. Pricing across venues

    An option with the same strike and expiry trades at different prices on different venues because each has its own order book, forward, index, fees and margin rules; the fair comparison is at execution, after fees.

17. Expiration cycles

    Deribit, OKX and Bybit list crypto option expiries on overlapping cycles, daily, weekly on Fridays, monthly on the last Friday of the month and quarterly on the last Friday of March, June, September and December, all expiring at 08:00 UTC.

18. Exercise and assignment

    Exercise is the holder using an option's right to buy or sell at the strike, and assignment is the seller being required to fulfil it; the options on Deribit, OKX and Bybit are European and cash-settled, so exercise happens only at expiry, automatically, as a payment of intrinsic value.

19. Backtesting option strategies

    Backtesting replays a strategy over historical market data to see how it would have performed, entering and exiting at the prices of the time, and measures the result with statistics such as win rate, total P&L and maximum drawdown.