Convertible ARM
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A convertible adjustable rate mortgage will convert to a fixed-rate mortgage with different adjustments.There is usually a fee assocciated with converting an ARM to a fixed rate, and your fixed rate will usually be .25-.5% above what ever the going fixed rate is at that time. This feature is not available on all ARMs, it must be included in the original terms of the loan.
A construction loan may come with the ability to roll into a fixed rate mortgage after the construction period is over. A "Conversion Option" is different than a Convertible Loan. A "conversion option" gives the borrower the ability to decide if converting to a fixed rate is more advantageous.