value = value.setScale(2, RoundingMode.CEILING)

I think that the RoundingMode you are looking for is HALF_EVEN. From the javadoc:

Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for ROUND_HALF_UP if the digit to the left of the discarded fraction is odd; behaves as for ROUND_HALF_DOWN if it's even. Note that this is the rounding mode that minimizes cumulative error when applied repeatedly over a sequence of calculations.

Here is a quick test case:

CopyBigDecimal a = new BigDecimal("10.12345");
BigDecimal b = new BigDecimal("10.12556");

a = a.setScale(2, RoundingMode.HALF_EVEN);
b = b.setScale(2, RoundingMode.HALF_EVEN);

System.out.println(a);
System.out.println(b);

Correctly prints:

Copy10.12
10.13

UPDATE:

setScale(int, int) has not been recommended since Java 1.5, when enums were first introduced, and was finally deprecated in Java 9. You should now use setScale(int, RoundingMode) e.g:

setScale(2, RoundingMode.HALF_EVEN)

BigDecimal is immutable, any operation on it including setScale(2, BigDecimal.ROUND_HALF_UP) produces a new BigDecimal. Correct code should be:

BigDecimal bd = new BigDecimal(1);
bd.setScale(2, BigDecimal.ROUND_HALF_UP); // this does NOT change bd
bd = bd.setScale(2, BigDecimal.ROUND_HALF_UP);
System.out.println(bd);

Output:

1.00

Note:

Since Java 9 BigDecimal.ROUND_HALF_UP has been deprecated and you should now use RoundingMode.HALF_UP.

Well this one works...

double roundOff = Math.round(a * 100.0) / 100.0;

Output is

123.14

Or as @Rufein said

 double roundOff = (double) Math.round(a * 100) / 100;

this will do it for you as well.

Try the following code. It is rounding half-up as expected as normally defined. That is such that 0.49999999999999990<0.5 so rounds down because it rounds down below 0.5 (a half).

I believe the OP has misunderstood the rule and just needs to use the ordinary HALF_UP rounding mode.

public static void main (String[] args) throws java.lang.Exception
{
    
    BigDecimal value=new BigDecimal("49.3249999999999999990");
    BigDecimal mark=new BigDecimal("49.325");//Values less than this round down!
    BigDecimal down=new BigDecimal("49.32");
    boolean expectDown;
    
    if(value.compareTo(mark)<0){
        System.out.println(value + " is less than "+mark);
        System.out.println("So rounds down");
        expectDown=true;
    }else{
        System.out.println(value + " is greater than or equal to "+mark);
        System.out.println("So rounds up");
        expectDown=false;
    }
    BigDecimal result=value.setScale(2,RoundingMode.HALF_UP);
    System.out.println("Rounded to "+result);
    if(result.equals(down)==expectDown){
        System.out.println("As expected");  
    }else{
        System.out.println("NOT As expected!!!");
    }
}

Expected Output:

49.3249999999999999990 is less than 49.325
So rounds down
Rounded to 49.32
As expected