[Sorry, no real answer - just a few observations. But a comment seems inappropriate for formatting reasons.]

What version and build do you use?

Your Multiply procedure looks somewhat strange to me, as it uses both an out parameter and a identical return value. That's an an obvious redundancy. Whereas return values are used with functions, inout/out parameters (and optional result sets) are typical for procedures. So your procedure seems to mix up these features a bit – something that older SA versions tend to accept whereas newer ones will prevent.

As you basically want to use a simple mathematical function, I would recommend to use a function like:

create function multiply (in mult1 int, in mult2 int) returns int
begin
   declare res1 int;
   -- return value defaulting to 1 in case of NULL values as input
   Set res1 = isnull(mult1 * mult2, 1);
   return (res1);
end;

Using a function will additionally make the use inside a second procedure easier (and more comprehensible).

I still don't get the exact requirements (as said, treat this as mere remarks), but usually you can use a cursor loop when you have to call a procedure/function repeated times and each call has to be based on the previous call's return value.

(The situation is different when the calls of the procedure/function are independent of each other. Then you could simply embed a function call in a select list of a query or use the procedure with a so-called lateral procedure call in the FROM clause of a query.)

So inside your procedure Compute (again turned into a function) you might use a FOR statement as a very convenient cursor loop:

create function Compute (inID integer) returns int
begin
   declare EFac integer;
   declare retval integer;

for forLoop as crs cursor for
      select CouponAmount from AACoupons where AAItemID = InID order by AACouponID
      for read only
   do
      if EFac is null then
         set EFac=1;
      end if;
      set EFac = Multiply(CouponAmount, EFac);
   end for;

-- further computation (counting or whatever)...
   set retval = ...;
   return (retval);
end;

Note: All statements are untested but should give you a hint.

Additional answer for procedures with several out parameters (cf. Siger's comments):

Say, you need to compute an integer division and would like to get both the quotient and the remainder in one call. That cannot be done with a function, and so you might use something like the following:

create procedure int_division(in dividend int, in divisor int,
   out quotient int, out remainder int)
no result set
begin
   -- Note: error handling (e.g. divide by zero) is stripped for simplicity
   set quotient = dividend / divisor;
   set remainder = dividend % divisor;
end;

You would call that procedure in another procedure similar to the following block (note: the declare with initialization is new in a V12). Obviously, you have to declare variables in the outer procedure to use them as arguments for the out parameters ("Call by reference" in PL terms).

begin
   declare d1 int = 21;
   declare d2 int = 11;
   declare q int;
   declare r int;
   call int_division(d1, d2, q, r);
   select d1, d2, q, r;
end;