| 摘要: | 本論文藉由衍生性商品評價方法與應用來探討長壽風險與氣候風險之議題，其一為不為負權益保證之評價，另一為氣候衍生性商品之評價。
第一篇文章為探討英國不為負權益保證之評價方法與實證分析。為反應其商品所有之風險特性，本文在評價不為負權益保證時考量了房價報酬、利率及死亡率具有隨機之特性外並進一步考慮房價具有跳躍的現象。在實證分析上，我們發現英國房價報酬具有顯著跳躍、自我相關及波動叢聚之特性，故在房價模型本文延用Chan and Maheu (2002)所提出 Jump ARMA-GARCH 模型。在利率與死亡率隨機性方面，本文分別採用CIR模型(Cox et al.,1985)與CBD模型(Cairns et al.,2006)進行分析與模擬。最後，本文利用B?hlmann et al. (1996)所提出Conditional Esscher Transform進行不為負權益保證的理論評價，進而提供合理的商品價格。由數值分析結果發現，房價之跳躍現象，利率風險及死亡率風險等均會影響英國不為負權益保證價格，其中以利率風險影響最鉅。在模型風險方面，本文針對不同的房價模型進行分析比較如Black Scholes, Merton Jump, ARMA-GARCH, ARMA-EGARCH, Double Exponential Jump Diffusion, Jump ARMA-GARCH模型。
第二章文章為氣候衍生性商品之評價方法與實證分析。氣候影響著我們每日的生活及選擇並對全球經濟活動造成巨大的影響。因此，如何規避氣候風險便成為一個相當重要的課題。近年來，店頭市場與集中市場已成功推出許多氣候衍生商品來規避不利的氣候因素所造成的經濟損失，然而在眾多的氣候衍生商品中，最常被交易的標的資產為氣溫。透過觀察台灣每日日均溫之動態行為，本文進一步提出ARFIMA-SGARCH模型捕捉台灣每日日均溫之動態過程。其實證結果發現，ARFIMA-SGARCH在溫度的配適及預測能力皆比傳統溫度模型來的出色。最後，本文進一步利用Cao and Wei(2004)所提出定價模型對氣候衍生性商品進行評價。
This dissertation contains two essays on the valuations of derivative approach to further explore longevity risk and weather risk issue. One is valuing No-Negative-Equity-Guarantee (NNEG) and another is valuation of weather derivative.First Essay:
Pricing No-Negative-Equity Guarantees for Equity Release Products To reflect the risks involving with equity releasing products, this study considers stochastic house price returns, interest rates and mortality rates to price no-negative-equity guarantees (NNEG). Particularly, we investigate the jump effect with house price returns. Observing from the data of U.K. house returns with significant persistence jumps, autocorrelation and volatility clustering, we propose a jump ARMA-GARCH model. Assuming the interest rate dynamics follow the CIR model (Cox et al.,1985) and mortality rate dynamics based on CBD model(Cairns et al.,2006), we derive a risk neutral valuation framework for NNEG using the conditional Esscher transform technique developed by B?hlmann et al. (1996). The numerical analysis reveals that the jump effect with house price returns, interest rate risk and mortality rate risk can affect the cost of NNEG and the impact is as significant as that for interest rate risk. Moreover, we demonstrate the model risk on pricing NNEG by comparing various house price return models of Black-Scholes, Merton Jump, ARMA-GARCH, ARMA-EGARCH, Double Exponential Jump Diffusion, Jump ARMA-GARCH models. Second Essay:
Long Memory in Temperature: Detection, Modeling, and Valuation the Weather DerivativesWeather influences our daily lives and choices and has an enormous impact on economy activity. The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather derivative contracts. The valuation of such contracts require the development of appropriate model for the prediction of underlying weather variable. Within this framework, we propose the ARFIMA- SGARCH model in order to model the daily average temperature dynamic evolution, as we observed the temperature process. Our model show a significant improvement fitting and forecasting performance compare with traditional temperature model. Finally, we present an application related to the forecast and simulation of temperatures indices used for the valuation of weather derivative proposed by Cao and Wei (2004). |
