Over the past few decades, option pricing accuracy has always been a standard criterion in gauging the performance of model parameter estimates. However, as a primary concern for option market makers, option hedging activity receives much less attention than pricing. Since option hedging strives to eliminate risks of market makers' portfolio positions in practice, it might be a more sensible measure in evaluating model estimates. In the first part of this thesis, a parameter estimation procedure based on minimizing the risks accumulated over the lifetime of an option is proposed. More specifically, a loss function which involves option pricing and hedging strategies is first defined to evaluate the cumulative hedging error(CHE). Then, after a simulation study assuming the Black-Scholes(BS) model for stock dynamics and option prices, an estimation method based on minimizing CHE is compared with maximum likelihood estimation(MLE) and implied estimation under three different model settings: the Black-Scholes model, the Merton jump diffusion, and the Heston stochastic volatility model. This comparison is conducted using an empirical study consisting of multiple datasets of individual stocks and options spanning 2011-2014 with the back-testing procedure. The second part of this thesis tries to mitigate the model-dependent feature of the first part, allowing flexible smoothing spline estimates for the option pricing curves. There are shape constraints induced by the arbitrage-free conditions of pricing options. Therefore, the form of the smoothing spline is carefully chosen to satisfy the constraints. In addition, certain transformation to the inputs of the pricing curve is performed to reduce dimensions. Under such strict constraints, we propose an option pricing curve which is composed of a weighted average between the Black-Scholes pricing function and a constrained cubic spline function. The resulting pricing and hedging strategies generated by the weighted curve estimator are then used to evaluate the previously defined cumulative hedging error(CHE). The back-testing results show that in general, smaller cumulative hedging error for real equity market data is achieved by the proposed hedging error minimization method, compared with traditional estimation methods.