Hedging and Valuation of Longevity Swap with Counterparty Risk
|關鍵字:||長壽風險;長壽衍生性商品;長壽交換;交易對手風險;避險;longevity risk;longevity swap;longevity derivatives;counterparty risk;hedging|
Longevity swaps are the most popular instruments for life insurers that translate their longevity risk to the capital market. Longevity swaps are typically a bilateral contract and their values are determined by not only the reference longevity rates but also the financial positions of contracting parties. This paper develops a Merton-type structural model with stochastic interest rates to examine how the default risk, asset risk, the size of swap, and the size of both contracting parties affect the valuation and the hedging effectiveness of the longevity swap. For index-based longevity contracts, we further look into how basis risk affects the valuation and the hedging effectiveness. We set up the dynamics of assets and liabilities for both contracting parties in a multi-period environment with stochastic interest rates and specify the payoffs of longevity swaps. We then compute the spreads of longevity swaps in a risk-neutral pricing framework via the Monte Carlo simulation. Our results show how spreads and hedging effectiveness of the longevity swap change with default risk, size of the swap, basis risk, interest rate risk, and the relative size of contracting parties.