隨機利率波動性下對通貨膨脹衍生性金融商品定價

Abstract

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.