Concepts / Pricing: SVI → N(d2)

Pricing: SVI → N(d₂)

When you ask “what are the odds BTC is above $70k on Friday?”, DeepBookie reads the live market and answers with a real probability.

₿

BTC$69,180

N(d₂) · P(up)

$66k$68k$70k$72k$74k

In plain terms

The market has a volatility curve — how much traders expect the price to move. DeepBookie fits it with a model called SVI (Stochastic Volatility Inspired).
It converts that into a probability with N(d₂) — a standard Black-Scholes formula that turns volatility into a 0–100% chance.
Do that for every strike and you get the odds curve above.

That probability is the fair price of your bet. Higher odds cost more to buy; longer-shot odds pay more if they hit.

Tip

This is the same model behind the odds-curve widget in chat. Ask “what are the odds BTC closes above $70k?” to see it live.

In @deepbookie/predict-client’s math.ts:

upProbability(svi, forward, strike) computes a normalized distance d₂ and runs it through normalCdf() → a number from 0 to 1.
downProbability = 1 − upProbability.
buildCurve() samples ~25 strikes around the forward price to draw the smile.

All inputs are scaled ×1e9 (see Scaling & units); the probabilities come back as 0–1.