How can I get a cumulative product with Snowflake?

A trick suggested by Sterling Paramore: Add logs, and then exponentiate it:

with data as (select $1 x from values (1),(2),(3),(4),(5))

select x
    , sum(x) over(order by x) sum
    , exp(sum(ln(x)) over(order by x)) mult
from data

If a built-in function doesn't exist, it's usually possible to roll something custom using a User-Defined Table Function.

In this case:

CREATE OR REPLACE FUNCTION CUMULATIVE_PRODUCT(VALUE double)
    RETURNS TABLE (PRODUCT double)
    LANGUAGE JAVASCRIPT
    AS '{
        initialize: function(argumentInfo, context) {
           this.cumulativeProduct = 1;
        },
        processRow: function f(row, rowWriter, context){
           this.cumulativeProduct = this.cumulativeProduct*row.VALUE;
           rowWriter.writeRow({PRODUCT: this.cumulativeProduct});
        }
    }';

Example table:

create temp table sample_numbers as (
select 1 as index, 5.1::double as current_value
    union all
select 2 as index, 4.3::double as current_value
    union all
select 3 as index, 3.7::double as current_value
    union all
select 4 as index, 3.9::double as current_value
)

invoking the UDTF:

select index,current_value,PRODUCT as cumulative_product
from sample_numbers,table(CUMULATIVE_PRODUCT(current_value) over ())

Note the empty over() clause which forces Snowflake to do a single sequential run over the data instead of splitting it into parallel chunks