隨機利率波動性下對通貨膨脹衍生性金融商品定價

Pricing Inflation Derivatives Within Interest Rate Stochastic Volatility

潘柏丞(Bo-Cheng Pan)

指導教授 ： 李賢源

國立臺灣大學/管理學院/財務金融學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.01382

摘要

本文以Heston與Fong-Vasicek模型為基礎。Heston模擬物價指數，並結合Fong- Vasicek模擬名目利率，實質利率以及各自的波動率，其中各個隨機過程的相關性不為零。Heston模型可以捕捉在通貨膨脹選擇權中的波動性微笑與波動性偏離；Fong-Vasicek模型可以解決以往文獻利率波動度為deterministic的問題。本文將隨機過程推導致T Forward Measure之下，利用蒙地卡羅法評價通貨膨脹選擇權。

關鍵字

Fong-Vasicek模型 ； Heston模型 ； 隨機波動度 ； 外匯分析法 ； 通貨膨脹選擇權

並列摘要

We consider a Heston type inflation model in combination with a Fong-Vasicek model for nominal and real interests and their variance, in which correlations can be non-zero. Due to the presence of Heston dynamics our derived inflation model is able to capture the implied volatility smile/skew, which is present in the inflation market data. Fong-Vasicek model can capture the stochastic interest rate volatility which is deterministic in the previous papers. We derive the dynamic under T Forward measure, and use the Monte Carlo Simulation to price the inflation options.

並列關鍵字

Fong-Vasicek model ； Heston model ； Stochastic volatility ； Foreign Currency Analysis ； Inflation options

參考文獻

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