具對手違約風險之市場長壽交換評價

Abstract

本文介紹長壽風險市場的歷史及現今市場概況，並建立結構模型，利用蒙地卡羅模擬法評價具有交易對手風險的長壽交換。透過分析比較在自身資本結構、對手資本結構、對手資本風險、對手資產規模的改變下，對於長壽交換評價結果的影響，並討論長壽交換契約中，若交易對手之負債比例較高，則壽險公司應更加注意交易對手之資產風險。最後我們透過比較進行長壽交換契約對保險公司違約機率的影響，討論長壽交換是否達到避險的目的。

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.