Distribution and forward curve
Two charts of where the option market prices one symbol's future price, as a probability curve at one expiry and as a forward price at every expiry.
What it answers
Two charts show where the option market prices one symbol's future price.
- Distribution shows how likely each price is at one expiry, and how far that differs from a plain lognormal model.
- Forward Curve shows the price the market sets for the stock at each expiry, compared with today's stock price.
How to read it
- 1The Distribution header. Its menu contains Tenor and Compare.
- 2The filled line is the implied probability distribution, one value per strike. The dashed line is the lognormal reference. Spot and Fwd mark two strikes.
- 3The Forward Curve header. Its menu contains Compare.
- 4Each dot is the forward price for one expiry, in dollars, shortest expiry on the left. The solid Spot line marks today's stock price.
Implied distribution
The implied distribution is computed from call prices by the Breeden-Litzenberger relation: the curvature of the call price across strikes gives the probability density. The call prices come from the fitted volatility surface. When that surface is missing, stale or blocked, they come from the ORATS smoothed implied volatility. The curve is scaled so that the area under it is 1, so its height is a chance per dollar of price. A value of 0.300% at a strike means about a 0.3% chance that the price finishes within one dollar of that strike at expiry.
These are risk-neutral probabilities, derived from market prices. They are not a forecast. When the curve has more weight on the left than the lognormal line, the market pays more for downside protection than the model implies.
Lognormal line
The lognormal line assumes that the price at expiry is lognormal, centred on the forward, with the at-the-money implied volatility. The at-the-money implied volatility is the fitted surface volatility at call delta 0.50 for the expiry. When the fitted surface is not available, it is the ORATS smoothed volatility at the listed strike whose delta is nearest 0.50. Where the implied curve is above the lognormal line, the market prices that range as more likely than the model does.
Spot and Fwd
Spot marks the listed strike nearest today's stock price. Fwd marks the strike nearest the forward for that expiry. Both lines are drawn at a listed strike. A strike with no positive density has no point on the curve.
Status dots
A dot in the top-right corner of the Distribution chart marks a density built from fallback inputs. Hover a dot to see its cause.
- Filled amber dot: the density is priced from ORATS smoothed volatility. The fitted volatility surface was missing, stale or blocked.
- Hollow blue ring: the forward fell back to spot. No put-call parity forward exists for this tenor, so Fwd marks the strike nearest spot.
The Dist Stats Panel shows the same dots.
Forward price
The forward for each expiry is computed by put-call parity at the strike whose delta is nearest 0.50. It is the strike plus the call price minus the put price, carried at the interest rate. A curve above the Spot line means the interest rate is above the dividend yield. A curve below it means the dividend yield is higher.
The Forward Curve draws every expiry from 5 to 365 days that has at least 10 strikes. The axis labels are days to expiry.
Axis spacing
Both horizontal axes space points evenly, whatever the distance between the values. On the Distribution chart, strikes $1 apart near the money take as much room as strikes $5 apart in the tails. This stretches the middle of the curve. On the Forward Curve, a 7-day gap between weekly expiries takes as much room as a 100-day gap between long expiries.
The data updates once a day before the open, so both charts show the previous trading day.
Controls
Open a chart's menu to change its view. Neither chart has header chips.
- Tenor: select 7, 14, 30, 60 or 90 days. The chart draws the available expiry nearest that number of days.
- Compare: draws up to three symbols on one axis.
- On the Distribution chart, Compare switches the axis to moneyness, rounded to 1%.
- Moneyness is the strike as a percent of the stock price.
- On the Forward Curve, Compare draws one line per symbol on one dollar axis.
- An expiry that one symbol lacks is a gap in that symbol's line.
Use the header search to select the symbol.
| Control | What it does |
|---|---|
| Distribution | |
| tenor | Tenor, which expiry the curve draws |
| Forward Curve | |
Use it with
- The Dist Stats Panel shows the implied price percentiles, tail probability and shape of the same distribution as numbers.