Essays in Finance
Date Issued
2011
Date
2011
Author(s)
Chou, Ying-Yin
Abstract
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.
Subjects
Stochastic volatility
TIPS
Embedded option
Inflation Risk
Indexed Bond
Dynamic Portfolio Choice
Elasticity of Inter-temporal Substitution
Type
thesis
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