The article presents a new method to quickly and accurately calculate prices for compound options in financial markets. By incorporating different time scales for volatility factors, the researchers developed a model that is not sensitive to specific market conditions. They used perturbation techniques to approximate the price of compound options based on constant volatility, with corrections for stochastic volatility effects. These corrections are based on universal parameters derived from implied volatility data. The method significantly reduces the time and effort needed for calibration and computation compared to traditional models.