The article discusses how to price Vanilla options in a market with changing volatility. By using a specific mathematical function for the volatility drift, researchers were able to find a way to calculate option prices accurately. This method involves choosing a measure where the volatility drift is zero, which is possible thanks to the Girsanov theorem. Even though these market models are not complete, researchers found a way to determine option prices in a straightforward manner. The popular Heston's model is one example where this technique can be applied to calculate option prices efficiently.