Although stochastic volatility models and local volatility model are very popular among the market practitioner for exotic option pricing and hedging, they have several critical defects both in theory and practice. We develop a new methodology for equity exotic option pricing and hedging within the marketbased approach framework. We build stochastic factor models for the whole surface of European call option prices directly from the market data, and then use this model to price exotic options, which is not liquidly traded. The factor models are built based on Karhunen-Loeve decomposition, which can be viewed as an infinite dimensional PCA. We develop the mathematical framework of centered and uncentered versions of the Karhunen-Loeve decomposition and study how to incorporate critical shape constraints. The shape constraints are important because no static arbitrage conditions should be satisfied by our factor models. We discuss this methodology theoretically and investigate it by applying to the simulated data.