Relish the Moment

Tucked away in our subconscious is an idyllic vision. We see ourselves on a long trip that spans the continent. We are traveling by train. Out the windows,     

Moment swaps

In this paper we discuss moment swaps. These derivatives depend on the realized higher moments of the underlying. A special case is the nowadays popular variance swaps. After introducing moment swaps we discuss how to hedge these derivatives. Moreover, we show how the classical hedge of the variance swap in terms of a position in log-contracts and a dynamic trading strategy can be significantly enhanced by using third moment swaps.     

Moment relations for some discrete distributions

Summary

Recursion relations for moments not involving differentiation with respect to the parameter of the distribution are given for the Poisson distribution in Philipson (1963) and those for the logarithmic series distribution in Patil, Kamat and Wani (1964) and Patil and Wani (1965). Similar results are obtained here for the negative binomial distribution. The relations referred to above are obtained as corollaries.     

Moment explosions in stochastic volatility models

In this paper, we demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than 1 can become infinite in finite time. As arbitrage-free price computation for a number of important fixed income products involves forming expectations of functions with super-linear growth, such lack of moment stability is of significant practical importance. For instance, we demonstrate that reasonably parametrized models can produce infinite prices for Eurodollar futures and for swaps with floating legs paying either Libor-in-arrears or a constant maturity swap rate. We systematically examine the moment explosion property across a spectrum of stochastic volatility models. We show that lognormal and displaced-diffusion type models are easily prone to moment explosions, whereas CEV-type models (including the so-called SABR model) are not. Related properties such as the failure of the martingale property are also considered.

---

Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.      

风口浪尖上的威廉·唐纳森

2002年,安然、世通等公司的财务丑闻沉重地打击了投资者信心,美国SEC前任主席哈维·皮特就是因处理不当而备受牵连,被迫在上任仅15个月后于去年11月5日提交了辞呈.当月10日,布什总统正式提名71岁的华尔街著名投资银行家威廉·唐纳森为第27任主席候选人.2月18日,他正式就任.     

On the Distributional Conditions for a Consumption-oriented Three Moment CAPM

In this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption-oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption-oriented CAPM.     

Fourth Moment Structure of Multivariate GARCH Models

This article derives conditions for the existence of fourthmoments of multivariate GARCH processes in the general vectorspecification and gives explicit results for the fourth momentsand autocovariances of the squares and cross products. Resultsare provided for the kurtosis and cokurtosis between components.Applications of the results include the definition of impulseresponse functions for kurtosis and cokurtosis, the derivationof the spectral density matrix of the squares and cross products,and a measure for causality in volatility. A bivariate exchangerate example illustrates the applications.     

文化产业投资正逢其时

文化产业是我国社会及经济发展的亮点和重要成分,是助推经济结构调整、加速经济发展模式转变的重要领域,发展前景灿烂。把握住时机的文化企业将快速成长并为其投资者提供丰厚回报。文化产业投资模式多样,VC、PE、并购等投资模式可以为处于初创期、成长期、成熟期的企业满足其不同的发展需求,另类投资作为资产配置的一种选择将逐步得到市场的认可,发展前景广阔。为了进一步促进文化产业的发展和文化投资的繁荣,国家应当鼓励文化行业向民间资本进一步开放;应重视投资交易风险控制、完善监管机制;进一步完善法律、税收等相关政策支持。     

Pricing CIR Yield Options by Conditional Moment Matching

We propose an approximation scheme for the pricing of yield options in the CIR model using conditional moment matching based on the gamma and lognormal distributions. This method is fast and simple to implement, and it shows a high degree of accuracy without being subject to the numerical instabilities that can be encountered with more sophisticated approaches.     

The Finite Moment Log Stable Process and Option Pricing

We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.     

Moment generating functions of compound renewal sums with discounted claims

Léveillé & Garrido (2001a, 2001b) have obtained recursive formulas for the moments of compound renewal sums with discounted claims, which incorporate both, Andersen's (1957) generalization of the classical risk model, where the claim number process is an ordinary renewal process, and Taylor's (1979), where the joint effect of the claims cost inflation and investment income on a compound Poisson risk process is considered.

In this paper, assuming certain regularity conditions, we improve the preceding results by examining more deeply the asymptotic and finite time moment generating functions of the discounted aggregate claims process. Examples are given for claim inter-arrival times and claim severity following phase-type distributions, such as the Erlang case.     

A Reexamination of the Relationship Between Preferences and Moment Orderings by Rational Risk-Averse Investors

This article examines the relationship between risk, return, skewness, and utility-based preferences. Examples are constructed showing that, for any commonly used utility function, it is possible to have two continuous unimodal random variables X and Y with positive and equal means, X having a larger variance and lower positive skewness than Y, and yet X has larger expected utility than Y, contrary to persistent folklore concerning U > 0 implying skewness preference for risk averters. In additon, it is shown that ceteris paribus analysis of preferences and moments, as occasionally used in the literature, is impossible since equality of higher-order central moments implies the total equality of the distributions involved.     

基于小波神经网络的高阶CAPM实证研究

本文在传统CAPM的基础上,引入了一个高阶的CAPM。借助小波神经网络在非线性函数逼近方面的优势,使用上海证券交易所股票数据分别对二阶至四阶CAPM进行了实证分析。最终的研究结果表明:就上海股市而言,12只大盘股组合已经能够有效分散非系统风险,而12只小盘股不能充分化解非系统风险,存在所谓的规模效应;训练后的网络预测显示,高阶CAPM无论是在预测精度还是预测稳定性上都要明显优于传统的CAPM,在一个非系统风险得到充分分散的证券组合中,加入三阶矩的CAPM已经能够比较准确地把握风险资产的市场定价。     

Using Four‐Moment Tail Risk to Examine Financial and Commodity Instrument Diversification

We consider the effect of higher moments on diversification, since most assets possess a potential for tail losses. In particular, we examine higher‐moment Value‐at‐Risk measures for individual instruments and diversified portfolios. We find that a naïve futures portfolio is consistently superior to common stock indexes. As few as ten randomly chosen instruments diversify away 85% of the unsystematic four‐moment tail risk. We also compare the two‐ and four‐moment tail risks for different size portfolios. Finally, the tail risk for naïve portfolios varies much less over time than other portfolios.     

Variance and Lower Partial Moment Measures of Systematic Risk: Some Analytical and Empirical Results

As a measure of systematic risk, the lower partial moment measure requires fewer restrictive assumptions than does the variance measure. However, the latter enjoys far wider usage than the former, perhaps because of its familiarity and the fact that two measures of systematic risk are equivalent when return distributions are normal. This paper shows analytically that there are systematic differences in the two risk measures when return distributions are lognormal. Results of empirical tests show that there are indeed systematic differences in measured values of the two risk measures for securities with above average and with below average systematic risk.     

"入世"机遇千载难逢应对挑战当务之急

肯定了中国入世是世界经济一化趋势所决定的，又对世贸组织的内涵条款及我国入世后面临的机遇与挑战进行了阐述，并探讨了我国应采取的对策。     

适应外汇管理理念与方式变革的举措探析

党的十八大以来,外汇管理的理念和方式发生了革命性变革,有效促进了贸易和投资便利化。但是在变革中,外汇指定银行的一些行为不利于外汇管理的开展,需要地方外汇管理部门和外汇指定银行共同应对予以解决。