Analysis of path-dependency in option value enhancement

Inspired by the market value enhancement concept of Conic hedging, we conduct an experiment to explore the contribution of path-dependency in discrete-time hedging to market value improvement of European vanilla options, in 3-step trinomial tree models. Our experiment values bid and ask prices improvement transforming hedging method from path-independent to path-dependent, under a family of exponential utility functions. To model a slightly more realistic hedging process than Conic finance, we introduce entropic risk measure to simulate the bid-ask spread of underlying in the actual market. The results show that, the improvement of bid and ask prices is not significant, under path-dependent hedging. However, we believe the model optimization in terms of optimizing algorithms and capacity of handling large data set current model is an intriguing topic worth further researching.