Discrete-time quadratic hedging and the computation of dynamic hedging ratios for options have been underexplored despite their importance in financial risk management. This master’s thesis presents two significant advancements in this area. First, a novel representation of the quadratic hedging ratio is introduced, allowing for the simultaneous computation of option prices and hedging ratios using efficient numerical methods without constraints on strike price spacing. Second, closed form recursive expressions for the cumulants of affine multi-factor models are derived, enabling a more accurate and computationally efficient implementation of the hedging strategy. Extensive numerical experiments, using models fitted on a comprehensive dataset of S&P 500 options from 1996 to 2018, demonstrate the effectiveness of these methods across various option maturities and strike prices. The results show substantial improvements in both computational speed and accuracy, offering a robust framework for risk management in complex financial markets.