Linear-quadratic term structure models – Toward the understanding of jumps in interest rates

We study linear-quadratic term structure models with random jumps in the short rate process where the jump arrival rate follows a stochastic process. Empirical results based on the US data show that incorporating stochastic jump intensity significantly improves model fit to the dynamics of both interest rate and volatility term structure. Our results also show that jump intensity is negatively correlated with interest rate changes and the average size is larger on the downside than upside. Examining the relation between jump intensity and macroeconomic shocks, we find that at monthly frequency, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with information shocks.     

Stock Crashes and Jumps Reactions to Information Demand and Supply: An Intraday Analysis

The objective of this paper is to examine the possible linkage between the intraday stock price crashes and jumps and public information by using data from the Chinese stock market and Baidu Index. We divided public information into two kinds of information: supply through online media and information demand across inquiries by individual investors. Using a large sample from Chinese listed firms from 2013 to 2019, our evidence clearly indicates that online information supply and demand both have a positive impact on the intraday crashes and jumps; this is, the firm with higher information supply and demand more likely to experience intraday crashes and jumps. The results are robust to an alternative measure of crash risk. Moreover, we further examine whether the market conditions have an impact on the relationship between information flow and intraday crashes and jumps, and find that the marginal effect of information supply on intraday price crashes and jumps is smaller in the bull market phase. Moreover, the bull market phase enhances the effect of information demand on intraday price crashes and jumps.

     

Optimal portfolios when volatility can jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.     

Super-Exponential RE bubble model with efficient crashes

We propose a dynamic Rational Expectations (RE) bubble model of prices, combining a geometric random walk with separate crash (and rally) discrete jump distributions associated with positive (and negative) bubbles. Crashes tend to efficiently bring back excess bubble prices close to a “normal” process. Then, the RE condition implies that the excess risk premium of the risky asset exposed to crashes is an increasing function of the amplitude of the expected crash, which itself grows with the bubble mispricing: hence, the larger the bubble price, the larger its subsequent growth rate. This positive feedback of price on return is the archetype of super-exponential price dynamics. We use the RE condition to estimate the real-time crash probability dynamically through an accelerating probability function depending on the increasing expected return. After showing how to estimate the model parameters, we obtain a closed-form approximation for the optimal investment that maximizes the expected log of wealth (Kelly criterion) for the risky bubbly asset and a risk-free asset. We demonstrate, on seven historical crashes, the promising outperformance of the method compared to a 60/40 portfolio, the classic Kelly allocation, and the risky asset, and how it mitigates jumps, both positive and negative.     

Option pricing under stochastic volatility and tempered stable Lévy jumps

The purpose of this paper is to introduce a stochastic volatility model for option pricing that exhibits Lévy jump behavior. For this model, we derive the general formula for a European call option. A well known particular case of this class of models is the Bates model, for which the jumps are modeled by a compound Poisson process with normally distributed jumps. Alternatively, we turn our attention to infinite activity jumps produced by a tempered stable process. Then we empirically compare the estimated log-return probability density and the option prices produced from this model to both the Bates model and the Black–Scholes model. We find that the tempered stable jumps describe more precisely market prices than compound Poisson jumps assumed in the Bates model.     

The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management

In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.     

Re-examining the investment-uncertainty relationship in a real options model

The main purpose of this paper is to re-examine the investment-uncertainty relationship in a real options model, and demonstrates that the Sarkar (J Econ Dyn Control 24:219–225, 2000) model is a special case of our model. This paper uses a general dynamic process, which incorporates mean reversion and jumps in a firm’s project earnings. We further derive a quasi-analytical form solution for the critical investment value and investment probability of a firm’s projects. From the simulation results, we find that an increase in uncertainty can always lead to an increase in the probability of investment, and thus has a positive impact on investment. These results, which differ from the findings of Sarkar (J Econ Dyn Control 24:219–225, 2000), could be explained by the mean-reversion and jump effects on a firm’s earnings.     

Option prices as probabilities

Four distribution functions are associated with call and put prices seen as functions of their strike and maturity. The random variables associated with these distributions are identified when the process for moneyness defined as the stock price relative to the forward price is a positive local martingale with no positive jumps that tends to zero at infinity. Results on calls require moneyness to be a continuous martingale as well. It is shown that for puts the distributions in the strike are those for the remaining supremum while for calls, they relate to the remaining infimum. In maturity we see the distribution functions for the last passage times of moneyness to strike.     

Investment intensity of currencies and the random walk hypothesis: Cross-currency evidence

This paper studies the cross-currency and temporal variations in the random walk behavior in exchange rates. We characterize currencies with relatively large investment flows as investment intensive and conjecture that the more investment intensive a currency is, the closer its exchange rate adheres to random walk. Using 29 floating bilateral USD exchange rates, we find that the higher the investment intensity, the less likely it is to reject random walk and the smaller the deviation from random walk is. However, the effect of investment intensity is non-monotonic. Application of threshold models shows that after investment intensity reaches the estimated thresholds, the level of investment intensity has no further effect on the deviation from random walk. These findings help reconcile the previous conflicting results on the random walk in exchange rates by focusing on the effect of cross-currency and temporal variations in investment intensity.     

Cojumps in stock prices: Empirical evidence

We examine contemporaneous jumps (cojumps) among individual stocks and a proxy for the market portfolio. We show, through a Monte Carlo study, that using intraday jump tests and a coexceedance criterion to detect cojumps has a power similar to the cojump test proposed by Bollerslev et al. (2008). However, we also show that we should not expect to detect all common jumps comprising a cojump when using such coexceedance based detection methods. Empirically, we provide evidence of an association between jumps in the market portfolio and cojumps in the underlying stocks. Consistent with our Monte Carlo evidence, moderate numbers of stocks are often detected to be involved in these (systematic) cojumps. Importantly, the results suggest that market-level news is able to generate simultaneous large jumps in individual stocks. We also find evidence of an association between systematic cojumps and Federal Funds Target Rate announcements.     

Power and Bipower Variation with Stochastic Volatility and Jumps

This article shows that realized power variation and its extension,realized bipower variation, which we introduce here, are somewhatrobust to rare jumps. We demonstrate that in special cases,realized bipower variation estimates integrated variance instochastic volatility models, thus providing a model-free andconsistent alternative to realized variance. Its robustnessproperty means that if we have a stochastic volatility plusinfrequent jumps process, then the difference between realizedvariance and realized bipower variation estimates the quadraticvariation of the jump component. This seems to be the firstmethod that can separate quadratic variation into its continuousand jump components. Various extensions are given, togetherwith proofs of special cases of these results. Detailed mathematicalresults are reported in Barndorff-Nielsen and Shephard (2003a).     

The role of audit verification in debt contracting: evidence from covenant violations

We investigate the role of audit verification in the resolution process following debt covenant violations. Using two sets of proxies for demand—audit fees and the independence and diligence of audit committees—we find evidence that covenant violations result in a demand for differentially higher levels of audit verification. Further analyses demonstrate the link between the increased demand for audit verification and the mechanisms designed to control agency costs in debt contracts. We document cross-sectional variations in the observed fee differential with respect to the level of reliance on financial covenants, the type of covenants violated, and waiver decisions. Moreover, we find that the observed audit fee increases are associated with more favorable movements in borrowing costs and the adoption of more conservative investment policies post violation. Our findings suggest that covenant violations increase the demand for audit services to help control contracting costs post violation.     

On Jumps in Common Stock Prices and Their Impact on Call Option Pricing

The Black-Scholes call option pricing model exhibits systematic empirical biases. The Merton call option pricing model, which explicitly admits jumps in the underlying security return process, may potentially eliminate these biases. We provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of NYSE listed common stocks. However, we find no operationally significant differences between the Black-Scholes and Merton model prices of the call options written on the sampled common stocks.     

A general characterization of one factor affine term structure models

We give a complete characterization of affine term structure models based on a general nonnegative Markov short rate process. This applies to the classical CIR model but includes as well short rate processes with jumps. We provide a link to the theory of branching processes and show how CBI-processes naturally enter the field of term structure modelling. Using Markov semigroup theory we exploit the full structure behind an affine term structure model and provide a deeper understanding of some well-known properties of the CIR model. Based on these fundamental results we construct a new short rate model with jumps, which extends the CIR model and still gives closed form expressions for bond options. Manusript received: June 2000, final version received: October 2000     

城市老年人社区养老服务需求特征与对策——基于吉林市的调查

我国人口老龄化形势严峻,养老服务需求问题成为政府和社会关注的重点问题。区域经济发展不平衡决定了不同城市的养老服务需求工作开展不同步。本文采用问卷调查方式,面向吉林市离退休职工,就生活照料、医疗护理、安全保障、精神慰藉以及社会参与等五个方面对城市社区养老需求进行调查分析。统计和分析结果表明,城市老年人对专业化程度高、有专门管理机构、有持续资金投入的社区养老服务有较高需求,对社区医疗护理服务和精神文化生活服务强烈关注。在此基础上,提出改进和完善城市社区养老服务体系建设的相关对策和建议。     

货币政策、消费品和投资品通货膨胀——基于金融加速器视角

本文建立一个包含消费品和投资品生产的两部门新凯恩斯DSGE模型,并且引入金融加速器以分析货币政策对消费品和投资品通货膨胀的影响机制,同时使用1999Q1至2015Q4的中国宏观经济数据对模型进行贝叶斯估计。估计结果表明,两个部门的菲利普斯曲线都具有较高的价格粘性。外部融资溢价对两个部门企业投资的影响存在异质性,投资品部门的金融加速器效应更加明显。脉冲响应分析表明货币政策扩张时,投资品部门的产出和通胀膨胀上升幅度比消费品部门更大。理论模型的脉冲响应与VAR实证分析得到的经验事实相一致。金融摩擦导致的消费品和投资品部门需求结构的异质性是解释货币政策对两个部门影响差异的关键。数值模拟分析发现金融加速器机制主要改变货币政策对投资品产出和通货膨胀的影响,对消费品部门影响改变较小。方差分解结果表明加总技术冲击、投资边际效率冲击和货币政策冲击是经济波动的主要来源。     

Modelling systemic price cojumps with Hawkes factor models

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating portfolios of highly liquid stocks, we find that there are a large number of high-frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one-factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets.     

Portfolio optimisation with jumps: Illustration with a pension accumulation scheme

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.