This thesis proposes a model to determine the maximum risk premium paid for a longevity swap by an insurer to hedge longevity risk in specic insurance contracts, considering Solvency II legislation.As longevity risk is an important risk factor next to nancial market risks, buying a hedge might be beneficial for insurers. In a longevity swap contract an insurer receives floating leg payments based on realized survival rates and makes predetermined fixed leg payments so that longevity risk in the insurance contract is hedged. As no liquid market for mortality-linked securities exists the risk premium for longevity risk is unknown. Here, Solvency II plays an important role. When Solvency II becomes effective insurers are, among others, obliged to maintain risk based capital buers and maintain a risk margin for unhedgeable risks such as longevity. The risk margin for longevity, an obligatory margin to raise the best estimate value of a specific insurance contract to a fair value, is assumed to represent the risk premium for longevity. The maximum premium to be paid for the swap is determined such that at inception of the swap contract, the fair value of the insurance contract when a swap is arranged does not exceed the fair value of the contract without the swap arrangement. This leads to a total risk premium which an insurer might pay as a lump sum at inception of the swap contract to its counterparty. But, as the premium in practice is likely included in the fixed leg payments, a method is proposed to spread out the lump sum premium over the fixed leg payments the insurer is obliged to make. TheLee-Carter stochastic mortality model is applied to determine best estimate mortality projections taking into account parameter uncertainty, required for modelling and projecting both legs of the swap. Results indicate that the premium is increasing with the amount of longevity risk in the insurance product.When default risk of the counterparty of the insurer in the swap contract is considered this has to priced by a risk margin as well, since longevity remains the underlying risk factor which cannot be hedged by financial instruments currently available in the market. The risk margin for default risk raises the fair value of the contract under the swap and decreases the value of the swap from the insurer’s perspective.Moreover, a decline in the creditworthiness of the counterparty has a negative effect on the premium as the effectiveness of the hedge deteriorates in case default of the counterparty is more likely to occur.