We consider the effect of stochastic parameters on the modelling of option prices. Our underlying asset model incorporates negative (down) and positive (up) jumps as well as stochastic volatility. Our empirical analysis with S&P 500 put options reveals that the parameters governing down jumps affect option price processes more significantly than those governing stochastic volatility or up jumps. However, due to the correlation structure between the model parameters and the underlying asset, stochastic volatility, up jumps, and down jumps affect our partial hedging almost in similar magnitude. A test of a portfolio selection strategy and different hedging scenarios shows that hedging parameter uncertainty improves the performance of a simple delta hedge on average by 8 percent and increases the portfolio’s Sharpe Ratio by 21 percent.