Model risk and discretisation of locally risk-minimising strategies

摘要

We consider two models for the price process: a time-continuous jump–diffusion and a time-discretisation of it. Then we study the robustness of the related locally risk-minimising strategy to this model choice where we focus mainly on hedging Asian and spread options. Using the discretisation scheme and the convergence results on backward stochastic differential equations as studied in Khedher and Vanmaele (2016), we show that the discrete-time locally risk-minimising strategies converge to the corresponding continuous-time strategies in an L2-sense. We present different numerical examples to illustrate our results.