Market Risk Modelling in the Solvency II Regime and Hedging Options Without Using the Underlying

Abstract

In the paper mathematical tools for quantile hedging in an incomplete market are developed. Those could be used for two significant applications. The first one is calculating the optimal capital requirement imposed by Solvency II when the market and non-market risks are present in an insurance company. We show how to find the minimal capital V0 to provide the oneyear hedging strategy for an insurance company satisfying mathbb(E) [ 1_({V_(1) ge D}) ] = 0.995, where V1 denotes the value of the company’s assets after one year, and D is the payoff of the contract. The second application is to find a hedging strategy for a derivative that does not use the underlying asset itself, but another asset whose dynamics are correlated with – or otherwise stochastically dependent on – those of the underlying. The paper generalises the results of obtained by Klusik and Palmowski in 2011.