The article compares different models for pricing options based on how they handle changes in volatility. Some models use constant volatility, while others allow for volatility to change over time. The non-constant volatility models considered are Dupire's local volatility and Hobson and Rogers path-dependent volatility models, which aim to keep the market balanced. On the other hand, stochastic volatility models like Heston and SABR are more flexible due to their two-factor nature. The study evaluates these models based on how well they match the implied volatility term structure and how effective they are in hedging and pricing various types of options.