You need to compare you values with DBNull.Value as follow
protected string PercentageChange(object client_Price, object second_price)
{
if(client_price==DBNull.Value)
{
.....
}
//double price1 = Convert.ToDouble(client_Price);
//double price2 = Convert.ToDouble(second_price);
//double percentagechange = ((price1 - price2) / price2) * 100;
//return percentagechange ;
}