Where could it land at expiry?

The risk-neutral probability distribution (Breeden-Litzenberger), centered on the real spot and built from NVDA's own realized volatility — where it could sit at expiry given how it's been moving, not a forecast. Here the vol level is a realized-vol estimate and the skew shape is modeled — not market-implied. With the mean/mode/median, the probability above vs below spot, an arbitrage-free check, with notes on the key figures.

NVDAspot $202.81realized vol 41.4%arbitrage-free ✓realized-vol estimate · skew modeledreal-time

Where it could land$179.99 – $230.19 — a 68% (1-σ) likely range at expiry, read off the implied distribution; spot $202.81.

implied densityspotmedian

Implied mean$203.50

Mode (most likely)$207.37

Median$204.12

P(below spot)47.8%

P(above spot)52.2%

Horizon30d

NVDA's realized volatility puts the most-likely landing near $207.37 with a $23.87 one-sigma swing, a left-skewed shape, and is arbitrage-free. The agent below explains how a vol surface becomes a probability distribution you can reshape and trade against. The vol level is a realized-vol estimate (the options chain is not entitled, so the skew shape is modeled, not market-implied); the Breeden-Litzenberger math is real. Your decisions, your risk.

Each card walks one piece of the distribution — what it shows, what the math means, and what it suggests — so a beginner can read (and edit) this realized-vol probability curve.

What is this probability distribution?

Built from NVDA's realized volatility, the most-likely landing is near $207.37 (the peak), with a mean of $203.50 and a one-sigma spread of about $23.87.

A volatility level + a strike grid, run through Breeden & Litzenberger (1978), becomes an entire probability distribution: line up call prices across strikes and the curvature of that line literally IS the density. The peak is the most-likely landing spot; the width is how uncertain the move is. Here the vol level is a realized-vol estimate (the options chain is not entitled, so it is not market-implied).

→ Most-likely close ~ $207.37; a realized-vol estimate of a $23.87 one-sigma swing.

How the skew bends the distribution

The distribution is left-skewed (fatter downside tail — more weight on a downside surprise) and close to a normal bell curve in the tails. Skewness -0.1532, kurtosis 3.0302.

A flat-IV (one number for every strike) world gives a clean lognormal bell. Real markets charge MORE implied vol for downside puts — that "skew" fattens the left tail of this curve, so the distribution leans toward downside surprises. The shape of the IV smile is the shape of the fear.

→ Downside protection is bid — the left tail is fat.

Is the curve arbitrage-free?

Yes — the call-price curve is convex everywhere, so every recovered probability is non-negative.

Probabilities can never be negative. Mathematically that requires the call-price curve to be CONVEX (bend upward) across strikes. If a middle call is too cheap relative to its neighbors, the second difference goes negative — a free-lunch "butterfly" arbitrage. The lab checks this automatically.

→ No-arbitrage: the implied density is valid.

Reshape it, then score your trade

Drag the curve to YOUR view (e.g. shift the peak higher if you are bullish) and the lab renormalizes it to a valid probability of 1.0, then scores any strategy you build against it.

This distribution is one estimate. If you think it is wrong, warp the curve to your own view — the lab keeps it a legal probability (area = 1) — then it integrates each strategy's expiry payoff against your curve to surface the positive-expected-value structures your thesis implies are mispriced.

→ Positive-EV hunting: where your view and this estimate disagree.

Glossary

Risk-neutral density: The probability distribution of where the stock lands at expiry, backed out from option prices (not a real-world forecast — it is the price-weighted one).
Breeden-Litzenberger: The 1978 result that the density equals e^{rT} times the second derivative of the call price with respect to strike.
Skewness: Asymmetry of the distribution; negative = fatter downside tail.
Kurtosis: Tail-fatness; above 3 means more extreme moves than a normal bell curve.
Butterfly arbitrage: A non-convex call curve implying a negative probability — a riskless mispricing.
Expected value (EV): The probability-weighted average P&L of a trade: payoff integrated against the distribution, minus cost.