財務金融研究

Essays in Finance

周盈吟(Ying-Yin Chou)

指導教授 ： 洪茂蔚

國立臺灣大學/管理學院/國際企業學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.02779

摘要

這篇論文主要是探討抗通膨債券的定價與投資者消費投資組合的最佳化解。在此篇論文的第一部分，我們在通膨率有隨機波動度下，得到一個美國抗通膨債券(TIPS)的解析解。在實證上，我們利用美國市場上的二十九支TIPS價格，求出在2000年一月到2009年十月期間，模型的未知參數和通膨利差。實證結果顯示，忽略隱含選擇權將導致通膨利差的高估。平均來說，高估的部分大概是0.82%。實證結果同時顯示，所得出的最小的利差發生在2009年一月附近，此時間點為本文探討期間發生最嚴重的通貨緊縮時點。在此篇論文的第二部分，我們解一個跨期消費投資組合問題當市場存在通膨風險時。投資人為了對抗通膨風險，會選擇持有抗通膨債券。本文說明，名目利率和通膨率如何影響最佳化消費財富的比例與跨期替代彈性有關。消費財富的比例不完全受到實質利率影響，同時也與名目利率和通膨率有關。最後，利用美國市場資料對模型做一個補正，結果顯示，積極型的投資者會想要擁有較多的名目債券以賺取通膨風險貼水，而保守型的投資者會持有較多的通膨債券以規避通膨風險。

關鍵字

隨機波動度 ； 美國抗通膨債券 ； 隱含選擇權 ； 通膨風險 ； 指數型債券 ； 投資組合選擇 ； 跨期替代彈性

並列摘要

The purpose of this thesis is to price the inflation indexed securities and solve for an inter-temporal portfolio consumption choice problem under inflation. In the first part of this thesis, a diffusion model for inflation rates with stochastic volatility is proposed, and closed-form solutions are derived for treasury inflation protected securities (TIPS). Empirically, our model with 29 TIPS, treasury constant maturity rates and reference CPI numbers in the U.S. market was used to derive the unknown parameters and spreads during January 2000 to October 2009. Empirical results show that an over-estimated spread is induced by ignoring the embedded option in TIPS. The average difference between the distorted estimate and actual value is about 0.82%. The minimum spread occurred around Jan. 2009 while the CPI-U decreased drastically. In the second part of this thesis, we solve for an inter-temporal portfolio consumption choice problem under inflation. The inclusion of the inflation-indexed bonds in the investor’s portfolio provides an opportunity to perfectly hedge against the inflation risk, while the hedging demand of the nominal bonds would be crowded out in proportion to the demand of the indexed bonds. The direction in which the interest rate and the inflation rate affect the optimal consumption-wealth ratio relies on the elasticity of inter-temporal substitution of the investor. The consumption wealth ratio is not completely determined by the real interest rate, it also depends on the nominal levels of the interest rate and the inflation rate. The capital market is calibrated to U.S. stock, bond, and inflation data. The optimal weights show that aggressive investors hold more nominal bonds to earn the inflation risk premium, and conservative ones concentrate on indexed bonds to hedge against the inflation risk.

並列關鍵字

Stochastic volatility ； TIPS ； Embedded option ； Inflation Risk ； Indexed Bond ； Dynamic Portfolio Choice ； Elasticity of Inter-temporal Substitution

參考文獻

Bates, D., 1996, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in PHLX Deutsche Mark Options”, Review of Financial Studies, 9, 69-107.

Brennan, M. J., 1998, “The Role of Learning in Dynamic Portfolio Decisions”, European Finance Review, 1, 295-306.

Brennan, M.J, Y. Xia, 2000, “Stochastic Interest Rates and the Bond-Stock Mix”, European Finance Review, 4, 197-210.

Brennan, M.J, Y. Xia, 2001, “Assessing Asset Pricing Anomalies”, Review of Financial Studies, 14, 905-942.

Brennan, M.J, Y. Xia, 2002, “Dynamic Asset Allocation under Inflation”, Journal of Finance, 57, 1201-1238.