This dissertation is devoted to high performance numerical methods for option valuation and model
calibration in L´evy process and stochastic volatility models. In the first part, a numerical scheme
for simulating from an analytic characteristic function is developed. Theoretically, error bounds
for bias are explicitly given. Practically, different types of options in commonly used L´evy process
models could be priced through this method fast and accurately. Also, sensitivity analysis could be
conducted through this approach effectively. Numerical results show that the schemes are effective
for both options valuation and sensitivity analysis in L´evy process models. In the second part, a
numerical scheme for Asian option pricing in jump-diffusion models is analyzed. Approximation
errors are shown to decay exponentially. Numerical results show the speed and accuracy of the
scheme. In the third part, for calibration purpose, certain numerical schemes are studied to price
European and American options. For European options, error bounds are explicitly given. For
American contracts, multiple options with different strikes and maturities could be priced simultaneously.
Numerical results show that the combination of the above schemes with state-of-the-art
optimization schemes makes efficient calibration of option pricing models possible
