Quadratic and Local Quadratic Hedging

This chapter introduces quadratic hedging to find the best approximation of the option in the sense of the mean-squared error among self-financing strategies. The exact solution for quadratic hedging can be given using backward induction. The chapter presents the solution in three steps: the single period model, the two period model and multiperiod model. It considers the pricing of an European option in the single period model. In the single period model quadratic hedging and local quadratic hedging are equivalent, but in the multiperiod models they are different. Local quadratic hedging applies a much simpler recursive scheme for minimizing the quadratic hedging error than global quadratic hedging. To implement quadratic hedging we use historical simulation. In Monte Carlo simulation a statistical model is imposed, and sequences of observations are generated from the model.