Stochastic durations,the convexity effect,and the impact of interest rate changes

This article shows that the equilibrium models of bond pricing do not preclude arbitrage opportunities caused by convexity. Consequently, stochastic durations derived from these models are limited in their ability to act as interest rate risk measures. The research of the present article makes use of an intertemporal utility maximization framework to determine the conditions under which duration is an adequate interest rate risk measure. Additionally, we show that zero coupon bonds satisfy those equilibrium conditions, whereas coupon bonds or bond portfolios do not as a result of the convexity effect. The results are supported by empirical evidence, which confirms the influence of convexity on the deviation of coupon bond returns from equilibrium.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model

This paper presents a method for estimating multi-factor versions of the Cox-Ingersoll-Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility.     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Intraday Empirical Analysis and Modeling of Diversified World Stock Indices

This paper proposes an approach to the intraday analysis of diversified world stock accumulation indices. The growth optimal portfolio (GOP) is used as reference unit or benchmark in a continuous financial market model. Diversified portfolios, covering the world stock market, are constructed and shown to approximate the GOP, providing the basis for a range of financial applications. The normalized GOP is modeled as a time transformed square root process of dimension four. Its dynamics are empirically verified for several world stock indices. Furthermore, the evolution of the transformed time is modeled as the integral over a rapidly evolving mean-reverting market activity process with deterministic volatility. The empirical findings suggest a rather simple and robust model for a world stock index that reflects the historical evolution, by using only a few readily observable parameters. Mathematics Subject Classification: (1991) primary 90A12, secondary 60G30,62P20 JEL Classification: G10, G13     

EXACT FORMULAS FOR PRICING BONDS AND OPTIONS WHEN INTEREST RATE DIFFUSIONS CONTAIN JUMPS

I develop Heath‐Jarrow‐Morton extensions of the Vasicek and Jamshidian pure‐diffusion models, extend these models to incorporate Poisson‐Gaussian interest rate jumps, and obtain closed‐form models for valuing default‐free, zero‐coupon bonds and European call and put options on default‐free, zero‐coupon bonds in a market where interest rates can experience discontinuous information shocks. The jump‐diffusion pricing models value the instrument as the probability‐weighted average of the pure‐diffusion model prices, each conditional on a specific number of jumps occurring during the life of the instrument. I extend the models to coupon‐bearing instruments by applying Jamshidian's serial‐decomposition technique.     

利率市场化对我国商业银行影响的实证分析

对于商业银行而言,利率市场化的积极意义在于它将促进金融市场的深化发展和金融机构之间的公平竞争,为银行业快速发展和多元化经营创造良好的外部环境。但是从短期来看,利率市场化也将改变商业银行原有的利率决定机制和经营模式。利率市场化将大大提高利率波动的幅度和频率,并使利率的期限结构复杂化,对商业银行的经营能力和风险把控能力都将是重大考验。本文选取10家国内上市商业银行,对其非利息收入占比、利率敏感性缺口等指标进行实证检验,最后根据实证结果对商业银行应对利率市场化提出合理建议。     

操作目标利率的选择与传导 ——基于MLF利率与隔夜利率的实证检验

依据2014-2018年月度数据,运用VAR模型考量MLF利率与隔夜利率对贷款加权利率、商业银行行为以及金融市场利率与金融市场波动的影响.结果表明:MLF利率对贷款加权利率和商业银行行为的影响较大,隔夜利率对金融市场利率和金融市场波动的影响较大.鉴此,应利用MLF利率调节贷款加权利率与商业银行行为,利用隔夜利率调节金融市场利率与金融市场波动,当两种利率的调节效果收敛接近时,再最终确定唯一的操作目标利率.     

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.     

A Complete Markovian Stochastic Volatility Model in the HJM Framework

This paper considers a stochastic volatility version of the Heath, Jarrow and and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model.     

A positive interest rate model with sticky barrier

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait for a random time until the rate is reinitialized to a (possibly random) strictly positive value. This setting ensures that all term rates are strictly positive.

Our objective is to provide a simple method to price zero-coupon bonds. A basic statistical study of the data at hand indeed suggests a switch to a different mode of behaviour when we get to a low level of interest rates. We introduce a variable for the time already spent at 0 (during the last stay) and derive the pricing equation for the bond. We then solve this partial integro-differential equation (PIDE) on its entire domain using a finite difference method (Cranck–Nicholson scheme), a method of characteristics and a fixed point algorithm. Resulting yield curves can exhibit many different shapes, including the S shape observed on the recent Japanese market.     

Decreasing Yield Curves in a Model with an Unknown Constant Growth Rate

The effect of incomplete information on the term structure ofinterest rates is examined in the framework of a pure exchangeeconomy under uncertainty where aggregate output grows at aconstant rate. If the growth rate is known, the term structure isflat. In contrast, the term structure is a decreasing curve whenagents do not know the growth rate. Long term yields are less thanthe short rate and the yield of long term bonds is determined bythe worst possible realizations of future short rates.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

2013年中国债券市场发展报告

2013年中国债券市场收益率曲线平坦化上行,高评级信用利差收窄,信用债等级间利差拓宽。展望2014年,资金面仍将维持紧平衡,利率债供给压力将小幅增加,国债收益率曲线小幅陡峭化下移,下半年市场表现好于上半年;在信用债市场,随着下半年市场收益率水平下行和信用债供给的增加,高评级产品利差将会拓宽;中低评级债券受信用风险事件和交易所重启IPO影响,等级间利差也将拓宽。     

我国利率市场化的目标、障碍和对策探讨

利率市场化的实现表现在两个层面上:一是在宏观层面上,表现为借贷市场资金的供求均衡决定利率总水平;二是在微观层面上,表现为具体融资项目的当事人根据项目的特点,通过协商或讨价还价,自主决定融资项目的利率.目前,我国整个利率体系的基准利率确定困难、商业银行风险定价能力不足以及利率市场化之后可能出现的存贷利差缩小是推进利率市场化进程的主要障碍.本文认为:我们应根据现有市场条件构建基准利率指标,为各具特点的融资项目提供合理的定价基础;商业银行应在市场建设的同时积极实践,以提高风险定价能力;商业银行之间应避免过度竞争,以保持合理利差.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

Understanding the Implied Volatility Surface for Options on a Diversified Index

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts. Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13