Market risk modelling in Solvency II regime and hedging options not using underlying

TL;DR

This paper develops mathematical tools for quantile hedging in incomplete markets, enabling insurance companies to calculate optimal capital requirements under Solvency II and hedge derivatives without directly using the underlying asset.

Contribution

It introduces a generalized approach to quantile hedging applicable to Solvency II capital calculations and hedging strategies involving non-tradable assets, extending prior work by Klusik and Palmowski.

Findings

Derived methods for minimal capital calculation under Solvency II

Proposed hedging strategies using correlated or dependent assets

Extended quantile hedging techniques to non-tradable assets

Abstract

In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC of the European Parliament and of the Council) when the market and non-market risk is present in insurance company. We show hot to find the minimal capital $V_0$ to provide with the one-year hedging strategy for insurance company satisfying $E\left[{\mathbf 1}_{\{V_1 \geq D\}}\right]=0.995$, where $V_1$ denotes the value of insurance company in one year time and $D$ is the payoff of the contract. o finding a hedging strategy for derivative not using underlying but an asset with dynamics correlated or in some other way dependent (no deterministically) on underlying. The work is a generalisation of the work of Klusik and Palmowski \cite{KluPal}. Keywords: quantile hedging, solvency II, capital modelling, hedging options on nontradable asset.