随着我国人口老龄化程度的不断加剧和养老金缺口的不断扩大，以及通货膨胀上行的压力，养老基金如何投资实现保值增值已经成为关系国家发展和社会稳定的重要课题。在此背景下本文构建了一个两因子连续时间定价模型，求解出风险中性测度下通胀指数债券的理论价格，并通过数值模拟分析了通胀指数债券对通货膨胀的抵御作用，以及名义利率、通货膨胀率、波动率和债券期限等因素对通胀指数债券价格的影响。研究表明：通胀指数债券价格与通货膨胀率、波动率正相关，与利率负相关，且波动率对通胀指数债券的影响系数要大于通货膨胀率，更大于利率；当预期通货膨胀率高于利率时，通胀指数债券会溢价发行，而且期限越长价格越高。本文的研究为养老基金多元化投资规避通胀风险、实现保值增值提供了可能，也为国家推进金融衍生工具的创新提供依据。
Along with the deepening of our country population aging degree, the expansion of the pension gap, and the inflation upward pressure, how pension fund invests to realize the value has become an important subject relations of the national development and social stability. Inflation-indexed bonds are viewed as an important tool to resist inflation risk, but there are no inflation-indexed bonds in China. Under this background, a two factor continuous time pricing model characterized by two fundamental variables is developed:the instantaneous inflation rate i(t) and the instantaneous nominal risk-free interest rate r(t), both follow the standard Vasicek model. Such a starting point differences this paper from previous related literature and is motivated by the economic reason that inflation rate and interest rate can both become negative. Based on these assumptions, the theoretical explicit solution of inflation-indexed bonds price under the risk neutral measure is got, and the numerical simulation is used to analyze the resistant effect of inflation indexed bonds on inflation, and the effect of the nominal interest rate, inflation rate, volatility and maturities on inflation-indexed bonds prices, using rolling regression and seemingly unrelated regression(SUR) method to estimate relevant parameters. The data window ranges from January 4, 2002 to January 4, 2016, a total of 5114 daily data. Research shows that the inflation-indexed bonds prices are positively with inflation rate and volatility, negatively with the interest rate, and the effect of volatility is greater than inflation rate and more than the interest rate. If the expected rate of inflation is higher than interest rates, inflation-indexed bonds will be issued at a premium, and the longer the maturities, the higher the prices. This paper makes it possible to price asset under the condition of negative inflation rate and interest rate, provides the possibility for the diversified investments of pension fund to avoid inflation risk and increase the value, and also provides the basis for the countries to promote the innovation of financial derivatives.
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