I believe I've read a story somewhere...

It said that 500 years ago, (making Pearl and Anna around the same age as Katherine), while Katherine was a freshly turned vampire, like few years into that, Pearl came up to her for help, as every medicine she tried to use on her deadly sick family failed, and she knew that Katherine never fell sick

Pearl's husband and Anna's siblings already died, Anna was on her deathbed, so Katherine decided to turn Anna and Pearl so they never fall sick again.

It was also stated that Pearl has 400 years on damon, implying that she's around Katherine's age, and if Anna's her biological daughter, that would make anna around the same age as her. Someone mentioned Anna and Damon came to a draw while they "choked eachother" But I'd like to remind that certain emotions amplify vampire's strenght. when Pearl DRAGGED Damon, she was pissed off - when Damon and Anna "fought", they felt no certain emotions.

Also, like mentioned in the season 3, Pearl and Anna knew about a weapon that could kill an original, and she knew of Mikael- For safety reasons/leverage, Pearl never told Katherine about it, So I wouldn't be even sure Pearl/Anna were turned by Katherine as implied in that short backstory i mentioned

So I say Pearl and Anna are biological mother and daughter, and they're over 500 years of age, turned by a newbie vampire Katherine.