# Price Probability Distribution

The following functions can be used for estimating
the future price development from the current trading prices of option
contracts. The result is a distribution of the cumulative price probability
at expiration time. The height of a bar in the image below is the probability
that the underlying price will end up at or below the given price level, in the
implied opinion of option traders.

SPY 2018,
cumulative price probability distribution ## contractCPD (int Days): int

Generates a cumulative robabililty distribution of the current asset price at
the given number of days in the future, and stores it internally. The
contractUpdate function must be called before.
** **
## cpd(var Price): var

Returns the cumulative probability of the given price.
The future price will be at or below the given
value with the returned probability in percent. The **contractCPD**
function must be called before.
## cpdv(var Percentile): var

Returns the price at the given percentile of the distribution. F.i. cpdv(50)
returns the median of the price distribution, with equal probability of a higher
or lower price.

### Parameters:

**Days** |
Minimum number of calendar days for which the price distribution is
estimated. Determines the expiration date of the used options. |

**Price** |
Underlying asset price to be estimated. |

**Percentile ** |
Probability that the future price is at or below the returned value. |

### Remarks:

- The probability distribution is derived from the ask, bid, and strike
prices of all option contracts at the determined expiration date. Since ask
and bid are subject to fluctuations, the resulting distribution can be
irregular.

### Example:

void main()
{
StartDate = 20170101;
BarPeriod = 1440;
PlotScale = 10;
assetList("AssetsIB");
assetHistory("SPY",FROM_STOOQ);
asset("SPY");
Multiplier = 100;
*// load today's contract chain*
contractUpdate(Stock,0,CALL|PUT);
var PriceCurrent = Contracts->fUnl;
printf("\nCurrent price %.2f",PriceCurrent);
*// what's the SPY price in 45 days?*
contractCPD(45);
var Price = 0.;
int i;
for(i = 0; i < 150; i++) {
Price += 0.01*PriceCurrent;
plotBar("CPD",i,Price,cpd(Price),BARS|LBL2,RED);
}
printf(", projected price %.2f",cpdv(50));
}

### See also:

contract, cdf

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