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研究生(外文):Chang, Po Neng
論文名稱(外文):Derivative Pricing Under Negative Interest Rate Environment
指導教授(外文):Lin, Shih Kuei
中文關鍵詞:負利率政策利率衍生性商品定價隨機波動度SABR 模型
外文關鍵詞:Negative Interest Rate PolicyInterest Rate Derivative PricingStochastic VolatilitySABR Model
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Negative rate in derivatives would be discussed in our thesis. Our main contribution is to provide the empirical results for these negative pricing model by negative interest rate market data. In addition, the experiment compares the performance between traditional pricing model and these negative pricing models by positive interest rate market data. Traditional pricing model could not work effectively and consistently under negative interest rate environment. Facing the challenge of negative interest rate policy, it is quite necessary for quants to develop the new perspective of pricing financial products and view of hedging the interest rate exposure. Several studies try to use the normal distribution instead of previous convention of the log normal assumption. Recently, both shifted diffusion and free boundary model have been widely introduced in related works. Thus, these approaches bring the new concepts and inspiration for some researchers. Furthermore, the stable and correct risk metrics is also a critical issue that market participants are concerned. Three modified SABR models from different literatures would be presented and calibrated by EUR market data and USD market data in this thesis. In the long run, there are some suggestions and future studies proposed in our work for the financial product pricing and risk management in a negative interest rate capital market.
1. 緒論 1
1.1 研究背景 1
1.2 研究目的 4
1.3 利率市場 5
1.4 數學工具 10
2. 正利率模型 14
2.1 Black模型 14
2.2 局部波動度 17
2.3 SABR模型 19
2.4 本章節結論 26
3. 負利率模型 27
3.1 常態分配模型 27
3.2 位移邊界模型 30
3.3 自由邊界模型 32
3.4 本章節結論 36
4. 模型的校準 37
4.1 資料與市場慣例 37
4.2 Cap的市場描述 38
4.3 校準波動度模型 40
4.4 實驗結果總整理 41
4.5 本章節結論 44
5. 結論與展望 45
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