Constructing a Bollinger Band target as a forward price

Restate the penetration as a forward target

A band-target construction restates a two-standard-deviation, 30-period Moving average penetration rule as the unknown next price that would make the close sit on the band. The system can then plot the trigger instead of guessing it.

The unknown price makes a quadratic

Because the unknown price enters both the Moving average and the standard-deviation term, the band-penetration equality is a quadratic. That quadratic can have one solution, two solutions, or no solution.

Lockout and a misleading single root

When the band retreats faster than price can reach it, the quadratic has no real root. The penetration rule is locked out, and the system cannot fire that period's signal.

A single-root case can still mislead a system if price later moves past the contact point. The construction then behaves as if the band was never reached.

Step the unknown price

The supplied construction finds the first feasible root by stepping the unknown price in 0.01 increments. It rebuilds the average and standard deviation at each step until the distance to the band is zero or stops shrinking.

Coarser step sizes speed the nested-loop search but reduce the accuracy of the solved target price.

Upper-band and lower-band targets are computed as separate procedures so the sign of the distance test and the direction of the price step stay consistent with each band.

What the construction returns

If a root exists the construction returns the target price, its percent change from the last close, and a flag of 1. If lockout occurs it returns the closest vertex price, the matching percent change, and a flag of 0.

Unsolved or hidden lockouts do not only suppress later trades. They also inject error into any backtest of the band-penetration system.

Archive testing associates lockout with unusually wide bands or unusually short Moving average lengths. Those construction choices need to be checked before a system is optimized.