通貨膨脹衍生性商品訂價方法之研究

Research on Pricing Methods of Inflation-Indexed Derivatives

羅雁文(Yen-Wen Lo)

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(2013年)

https://doi.org/10.6342/NTU.2013.10322

摘要

本文旨在引入Heston（1993）隨機波動度的概念，進而利用簡化後的Trolle and Schwartz（2009）隨機波動度模型，改善過去對通貨膨脹衍生性商品訂價，所使用的三因子無套利期限結構模型（the three-factor arbitrage-free term structure model）；用以更準確地捕捉利率波動度駝峰（volatility hump）的現象，並具有更好的訂價能力。此三因子模型，包含名目利率期限結構（the nominal term structure）、實質利率期限結構（the real term structure），及通貨膨脹指數的動態隨機過程（the dynamic of the inflation index）。隨機波動度模型的主要設定在於，其包含利率期限結構因子及非利率期限結構因子，亦考慮到利率波動度變化與利率變化之間的相關性，能更準確地描述市場上的利率動向。將此模型設定套入三因子模型之三要素，透過名目和實質測度下零息債券價格動態過程的推導與測度轉換，進一步探討通貨膨脹衍生性商品之訂價方法。

關鍵字

Trolle and Schwartz模型 ； 隨機波動度 ； 利率期限結構 ； 通貨膨脹三因子模型 ； 通貨膨脹衍生性商品

並列摘要

The objective of this paper is to apply the concept of the stochastic volatility in Heston (1993). That is, by adopting the simplified stochastic volatility model in Trolle and Schwartz (2009), the three-factor arbitrage-free term structure model can better capture volatility humps of interest rates. Therefore, the improved model can price derivatives more precisely. The three-factor model includes the nominal term structure, the real term structure, and the dynamic of the inflation index. The stochastic volatility model is composed of stochastic volatility factors and unspanned stochastic volatility factors, and concerned about the relation between the change in volatilities of interest rates and the change in interest rates. Thus, it can better describe the dynamics of interest rates in the market by substituting the stochastic volatility model for the previous ones in three-factor structure. With derivations of dynamics of both nominal and real zero coupon bond prices and changes of measures, we can further discuss pricing methods of inflation-indexed derivatives under this framework.

並列關鍵字

Trolle and Schwartz model ； stochastic volatility ； term structures of interest rate ； three-factor inflation model ； inflation-indexed derivatives

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