以Heston model隨機波動度模型評價結構型商品與目標可贖回遠期契約;Using Heston Model to Evaluate Equity Linked Note and Target Redemption Forward

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题名:	以Heston model隨機波動度模型評價結構型商品與目標可贖回遠期契約;Using Heston Model to Evaluate Equity Linked Note and Target Redemption Forward
作者:	夏漢權;Hsia, Han-Chiuan
贡献者:	財務金融學系
关键词:	Heston模型;參數校準;蒙地卡羅模擬;Heston model;Calibration;Monte Carlo simulations
日期:	2017-07-04
上传时间:	2017-10-27 13:49:33 (UTC+8)
出版者:	國立中央大學
摘要:	本文採用Heston (1993)發表之隨機波動度模型評價台指結構型商品與兩檔TRF，並對於模型之操作過程詳細說明。在參數校準上，利用最小平方法建立誤差函數，並使用價外買權與價外賣權共同建構隱含波動度曲線；本文亦採用歷史資料估計之相關係數來取代原先欲校準之模型參數rho，結果發現，在台指選擇權之校準中，能在不損失太多誤差下提升校準效率。本文後續針對台指選擇權、日圓兌美元選擇權、歐元兌美元選擇權之校準狀況作分析，並進一步觀察選擇權在不同到期日下，校準參數與隱含波動度曲線之關係；接著分析2016年發生之大事件對於參數校準造成之影響。最後，利用蒙地卡羅模擬法分析三種商品在BS模型與Heston模型模擬下的差異，結果發現在不同分配假設下，兩種模型模擬結果差異甚大。後續比較尤拉法切割期數對模擬產生之影響，研究發現，在模擬切割期數不同下結果會有些微差異，但考慮模擬效率下一天切割一期即為足夠。;The paper adopts the stochastic volatility model of Heston (1993) to evaluate equity linked note and target redemption forwards, and illustrates the operating step of model in detail. In the thesis, I use the least square method to calibrate parameters, and use out of the money calls and out of the money puts to build implied volatility curves. I also find that after replacing the correlation parameters with new correlation parameters estimated by historical data, the error of calibration slightly increases with improving the efficiency of calibration in TAIEX options. And then, I analyze the correlation between implied volatility curves and parameters in different maturities and different assets, namely TAIEX options, EUR/USD options and JPY/USD options. I also examine that how big events in 2016 affect my calibration results. In order to evaluate equity linked note and target redemption forwards, I perform Monde-Carol simulation to compare between BS Model and Heston Model to search if there is any difference between those popular option pricing theories, the discovery is that the winning probability of BS and Heston model are not the same because of its basic assumption. Last but not the least, I adopt Euler-method to distinguish different time space of simulation, and find that there is little difference between different time spaces.
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