氣候變遷導致極端高溫與異常氣候頻率升高，對臺灣高經濟果樹如蓮霧生產
構成實質威脅。傳統農業保險因存在資訊不對稱與道德風險問題，難以有效承擔
天災損失風險，指數型保險因其理賠依據明確且操作彈性高，逐漸成為農業保險
設計趨勢。
本研究以屏東地區蓮霧為對象，整合 2013 至 2023 年氣象與產量資料，建立
七項溫度指標，透過主成分分析（PCA）提取綜合氣候風險指標 PC1，並藉由
Gaussian Mixture Model 進行群集以統計方式推估理賠門檻 Rs 與 Rt，進而設
計線性遞減式理賠函數。為提升門檻設定之穩健性，本研究引入 Bootstrap 重抽
樣技術，計算出 Rs = −2.4091、Rt = −1.5545 為平均理賠門檻。
在保費估算上，本研究進一步以 ARMA 模型擬合 PC1 時序特性，並進行
蒙地卡羅模擬產生 10,000 筆未來氣候指標樣本，套入理賠函數估算期望理賠金
額並折現，結果得純保費為新台幣 108,789 元。相較於 Black-Scholes 模型因履
約機率過低導致保費低估，期望理賠折現法能更真實反映實際風險，具備實務應
用潛力。
本研究建構一套兼具氣候風險評估、門檻設定與保費精算的指數型保險架構，
對於未來發展適應型農業保險商品提供具操作性與可行性之設計參考。

Climate change has increased the frequency of extreme heat and abnormal weather
events, posing a substantial threat to the production of high-value fruit crops in
Taiwan, such as wax apples. Traditional agricultural insurance often struggles to
effectively cover natural disaster risks due to problems like information asymmetry
and moral hazard. In contrast, index-based insurance has emerged as a promising
solution, offering clear claim criteria and high operational flexibility.
This study focuses on wax apple production in Pingtung, Taiwan, utilizing
meteorological and yield data from 2013 to 2023. Seven temperature-based indices
were constructed, and Principal Component Analysis (PCA) was employed to extract
a composite climate risk indicator, PC1. To statistically estimate indemnity
thresholds Rs and Rt, a Gaussian Mixture Model (GMM) was applied for clustering.
A linearly decreasing indemnity function was then designed based on these
thresholds. To enhance the robustness of threshold estimation, a Bootstrap
resampling technique was introduced, yielding average thresholds of Rs = −2.4091
and Rt = −1.5545.
For premium estimation, this study further fitted an ARMA model to capture the
temporal characteristics of PC1 and conducted Monte Carlo simulations to generate
10,000 synthetic climate risk scenarios. These were input into the indemnity function
to calculate expected indemnity payments, which were then discounted. The resulting
pure premium was NT$108,789. Compared to the Black-Scholes model—which tends
to underestimate premiums due to a low probability of payout—the expected
6
indemnity discounting method more accurately reflects real-world risk and offers
greater practical applicability.
This research presents a comprehensive framework for index-based insurance design,
integrating climate risk assessment, threshold estimation, and actuarial premium
pricing. It provides a practical and feasible reference for the future development of
adaptive agricultural insurance products.

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