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。
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.
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