可解約分紅保單之遞迴評價公式

Bacinello（2003a）於固定利率之下評價分紅保單，此分紅保單包含分紅選擇權與解約選擇權，分紅選擇權可視為歐式選擇權，解約選擇權可視為美式選擇榷。本文在隨機利率模型下，提出二維度CRR模型，以評價分紅選擇權與解約選擇權，不但具有精確度與收斂性質，而且在計算上也十分有效率。此外，本文針對分紅係單中現金流量之前後關係，推導出遞迴關係式，以增進二維度CRR模型之計算速度。根據二維度CRR模型之遞迴公式，求得可解約分紅保單之公平價值，並討論各種參數對可解約分紅保單的影響，以利於保險公司評價可解約分紅保單之參考。

關鍵字

分紅係單；分紅選擇權；解約選擇權；二維度CRR模型

並列摘要

Bacinello (2003a) employed CRR model 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 CU model in a stochastic interest rate model as a means of providing a numerical method for contract pricing. The two-dimensional CU model converges rapidly and achieves similar results to Monte Carlo simulation. Two-dimensional CU 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.

並列關鍵字

Participating Policy ； participating Option ； surrender Option ； two-dimensional CRR Model

參考文獻

Albizzati, M.-O.,Geman, H.(1994).Interest Rate Management and Valuation of the Surrender Option in Life Insurance Policies.Journal of Risk and Insurance.61(4),616-637.

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Bacinello, A. R.(2001).Fair Pricing of Life Insurance Participating Polices with a Minimum Interest Rate Guaranteed.ASTIN Bulletin.31(2),275-297.

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Bacinello, A. R.(2003).Fair Valuation of a Guaranteed Life insurance Participating Contract Embedding a Surrender Option.Journal of Risk and Insurance.70(3),461-487.

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Bacinello, A. R.(2003).Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option.North American Actuarial Journal.7(3),1-11.