Hedging under liquidity constraints

Although risk management can be justified by financial distress, the theoretical models usually contain hedging instruments free of funding risk. In practice, management of the counterparty risk in derivative transactions is of enhanced importance, consequently not only is trading on exchanges subject to the presence of a margin account, but also in bilateral (OTC) agreements parties will require margins or collateral from their partners in order to hedge the mark-tomarket loss of the transaction. The aim of this paper is to present and compare two models where the financing need of the hedging instrument also appears, influencing the hedging strategy and the optimal hedging ratio. Both models contain the same source of risk and optimisation criterion, but the liquidity risk is modelled in different ways. In the first model, there is no additional financing resource that can be used to finance the margin account in case of a margin call, which entails the risk of liquidation of the hedging position. In the second model, the financing is available but a given credit spread is to be paid for this, so hedging can become costly.

Solvency risk minimizing guaranteed returns in life insurance

Return guarantee constitutes a key ingredient of classical life insurance premium calculation. In the current low interest rate environment insurers face increasingly strong financial incentives to reduce guaranteed returns embedded in life insurance contracts. However, return guarantee lowering efforts are restrained by associated demand effects, since a higher guaranteed return makes the net price of the insurance cover lower. This tradeoff between possibly higher future insurance obligations and the possibility of a larger demand for life insurance products can theoretically also be considered when determining optimal guaranteed returns. In this paper, optimality of return guarantee levels is analyzed from a solvency point of view. Availability and some other properties of optimal solutions for guaranteed returns are explored and compared in a simple model for two measures of solvency risk (company-level and contract-level VaR). The paper concludes that a solvency risk minimizing optimal guaranteed return may theoretically exist, although its practical availability can be impeded by economic and regulatory constraints.