Average payoffs for values of |$\kappa \in \{\hat{\kappa }, 2\hat{\kappa }, 5\hat{\kappa }, 10\hat{\kappa }\}$| (left) and HDD distribution for a derivative on the month of January 2019, forecasted 30 days ahead and based on |$50\,000$| Monte Carlo simulations (right). |$HDD_{strike}$| is kept at 90% empirical quantile of |$\kappa = \hat{\kappa }$| for all simulations.