Financial Terms - Renouncable Rights

What does it means...
An offer issued by a corporation to shareholders to purchase more shares of the corporation's stock (usually at a discount). Renounceable rights have a value and can be traded.

Investopedia says...
Stockholders that have received renounceable rights have three choices of what to do with the rights. They can act on the rights and buy more shares as per the particulars of the rights issue; they can sell them on the market; or they can pass on taking advantage of their rights.

Details found here.

Non-Renouncable Rights
What does it means...
An offer issued by a corporation to shareholders to purchase more shares of the corporation (usually at a discount). Unlike a renounceable right, a non-renounceable right is not transferable, and therefore cannot be bought or sold.

Investopedia says...
Issuing more shares dilutes the value of outstanding stock. But because the rights issue allows the existing shareholders to buy the newly issued stock at a discount, they are compensated for the impending share dilution - the compensation the rights issue gives them is equivalent to the cost of share dilution. However, shareholders who do not take exercise the rights by buying the discounted stock will lose money as their existing holdings will suffer from the dilution.

Details found here.

Underwriting for that rights would means that if the rights are not fully total up, the underwriting company will fulfill the quota.