The item creation rules certainly allow creation of cursed items. The DMG gives guidelines based on cost on pages 129 and 130.
The creation of a magic item is a lengthy, expensive task. To start, a character must have a formula that describes the construction of the item. The character must also be a spellcaster with spell slots and must be able to cast any spells that the item can produce. Moreover, the character must meet a level minimum determined by the item's rarity, as shown in the Crafting Magic Items table.
An item has a creation cost specified in the Crafting Magic Items table (half that cost for a consumable, such as a potion or scroll). A character engaged in the crafting of a magic item makes progress in 25 gp increments, spending that amount for each day of work until the total cost is paid. The character is assumed to work for 8 hours each of those days. Thus, creating an uncommon magic item takes 20 days and 500 gp.
\begin{array}{l | l | l} \text{Item Rarity} & \text{Creation Cost (gp)} & \text{Minimum Level} \\ \hline \text{Common} & 100 & 3rd \\ \text{Uncommon} & 500 & 3rd \\ \text{Rare} & 5,000 & 6th \\ \text{Very Rare} & 50,000 & 11th \\ \text{Legendary} & 500,000 & 17th \\ \end{array}
For example, creation of a very rare cursed item would cost 50k GP, require a special recipe, at 25gp per day per 11th level character. This would take 333 days for a six person party.
Generally, magical items of that power are meant to be found, not created.