Performance Evaluation of Discrete-Time Hedging Strategies for European Contingent Claims

We consider the use of discrete-time quadratic optimal hedging strategies for hedging European contingent claims (ECCs). Specifically, the objective of the current work is to numerically compare the effectiveness of two quadratic trading strategies with the standard delta hedging. The two quadratic optimal hedging strategies that we consider are mean-variance hedging in a risk-neutral measure and optimal local-variance hedging in a market probability measure. The objective function for the former is the variance of the hedging error calculated in a risk-neutral measure and the latter optimizes the variance of the mark-to-market value of the portfolio over a single trading interval in a market probability measure. The comparison is done on multiple performance measures such as the probability of loss, expected loss, different moments of the hedging error and shortfall measures such as value at risk (VaR) and conditional value at risk (CVaR). The performance evaluation results on path-independent and exchange like options conclude that in the discrete-time setting the quadratic optimal hedging strategies outperform the delta hedging strategy. Indeed, as the re-balancing is done more sparsely, the quadratic-optimal trading schemes fair better than the standard delta-hedging.