Fair Valuation of Participating Insurance Policies with Surrender Options

本文探討評價可解約分紅保單（Participating Policy）。該保單隱含二個重要的選擇權：分紅選擇權與解約選擇權。分紅選擇權為一歐式買權，解約選擇權可視為美式賣權。Bacinello（2003）使用CRR模型，計算解約選擇權的近似解，然而，Bacinello（2003）假設無風險利率為常數。本文主要探討如何利用無套利評價法，在隨機利率模型下，發展二維度之CRR模型，利用此模型，求得分紅選擇權與解約選擇權之公平價格，並討論利率的波動與長期走勢對該保單的選擇權的價格之影響。本文發現，保單之投資參考組合的波動，將對分紅選擇權的價格造成影響，而利率的波動會導致解約選擇權價格上升；當未來預期利率上升時，分紅選擇權與解約選擇權亦隨之上升。此評價模式可作為保險公司發行分紅保單與避險策略之參考。Bacinello (2003a) employed Cox-Ross-Rubinstein model (CRR model, 1979) to numerically calculate the fair value of a participating policy containing a surrender option. Bacinello assumed a constant rate of return on risk-free assets. However, this study proposes a two-dimensional CRR model in a stochastic interest rate model as a means of providing a numerical method for contract pricing. The two-dimensional CRR model converges rapidly and achieves similar results to Monte Carlo simulation. Two-dimensional CRR models are used to analyze the importance and sensitivity of a stochastic interest rate model for the policy. Zero coupon bond volatility is an essential parameter in the surrender option, and reference portfolio volatility is important for pricing the participating option. The participating and surrender options are more valuable given upwards trending interest rates than constant or downwards trending rates