MODEL‐INDEPENDENT LOWER BOUND ON VARIANCE SWAPS

It is well known that, under a continuity assumption on the price of a stock S, the realized variance of S for maturity T can be replicated by a portfolio of calls and puts maturing at T. This paper assumes that call prices on S maturing at T are known for all strikes but makes no continuity assumptions on S. We derive semiexplicit expressions for the supremum lower bound on the hedged payoff, at maturity T, of a long position in the realized variance of S. Equivalently, is the supremum strike K such that an investor with a long position in a variance swap with strike K can ensure a nonnegative payoff at T. We study examples with constant implied volatilities and with a volatility skew. In our examples, is close to the fair variance strike obtained under the continuity assumption.     

Return predictability of variance differences: A fractionally cointegrated approach

This paper examines the fractional cointegration between downside (upside) components of realized and implied variances. A positive association is found between the strength of their cofractional relation and the return predictability of their differences. That association is established via the common long-memory component of the variances that are fractionally cointegrated, which represents the volatility-of-volatility factor that determines the variance premium. Our results indicate that market fears play a critical role not only in driving the long-run equilibrium relationship between implied-realized variances but also in understanding the return predictability. A simulation study further verifies these claims.     

EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION

This paper develops an equilibrium asset and option pricing model in a production economy under jump diffusion. The model provides analytical formulas for an equity premium and a more general pricing kernel that links the physical and risk‐neutral densities. The model explains the two empirical phenomena of the negative variance risk premium and implied volatility smirk if market crashes are expected. Model estimation with the S&P 500 index from 1985 to 2005 shows that jump size is indeed negative and the risk aversion coefficient has a reasonable value when taking the jump into account.     

Oil jump risk

The risk premium associated with large upside jumps in oil market is a significant driver of the cross-section of stock returns from 1986 to 2014. In contrast to previous research, variance risk is priced only when we do not control for jumps. Upward jumps are priced in tight supply-demand conditions but not in more abundant supply periods. There is some evidence that downward jumps are priced in abundant supply conditions but not in tight conditions. Innovations in risk neutral jumps have predictive power for important economic indicators, including notably consumption growth. This helps explain the pricing of jump risks.     

Variance and skew risk premiums for the volatility market: The VIX evidence

We extract variance and skew risk premiums from volatility derivatives in a model-free way and analyze their relationships along with volatility index and equity index returns. These risk premiums can be synthesized through option trading strategies. Using a time series of option prices on the VIX, we find that variance swap excess return can be partially explained by volatility index and equity index excess returns while these latter variables carry little information for the skew swap excess return. The results sharply contrast with those obtained for the equity index option market underlining very specific characteristics of the volatility derivative market.     

Jump variance risk: Evidence from option valuation and stock returns

We study jump variance risk by jointly examining both stock and option markets. We develop a GARCH option pricing model with jump variance dynamics and a nonmonotonic pricing kernel featuring jump variance risk premium. The model yields a closed-form option pricing formula and improves in fitting index options from 1996 to 2015. The model-implied jump variance risk premium has predictive power for future market returns. In the cross-section, heterogeneity in exposures to jump variance risk leads to a 6% difference in risk-adjusted returns annually.     

The term structure of systematic and idiosyncratic risk

We study the term structure of variance (total risk), systematic, and idiosyncratic risk. Consistent with the expectations hypothesis, we find that, for the entire market, the slope of the term structure of variance is mainly informative about the path of future variance. Thus, there is little indication of a time-varying term premium. Turning the focus to individual stocks, we cannot reject the expectations hypothesis for systematic variance, but we strongly reject it for idiosyncratic variance. Our results are robust to jumps and potential statistical biases.     

Industry variance risk premium,cross-industry correlation,and expected returns

We investigate the variance risk premium (VRP) and implied correlation (IC) at the industry level. Using the index and sector exchange-traded fund options, we construct-sector VRPs and cross-sector IC measures. Sector VRPs predict sector returns, and adding the average sector VRP with IC improves predictability. Combining the average sector VRP and IC outperforms the market VRP in predicting market returns both in-sample and out-of-sample and generates sizeable economic values. We document a strong spillover effect from sector VRPs to the market VRP. The average sector VRP and cross-sector IC contain information beyond the market VRP and cross-stock IC.     

CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS

We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modeling. For the special cases of jointly normally and t‐distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Fréchet or Gumbel distribution. It turns out that correlations in heavy‐tailed NVM models are less sensitive to stress than in medium‐ or light‐tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy. We also demonstrate how our results can be applied for more prudent stress testing.     

贝塔系数是风险的正确度量吗

在经典的投资组合理论中 ,假设所有资产的报酬率服从对数正态分布 ,因而只需要用收益的方差来度量风险就足够了 ,忽略了偏度的影响。资产收益的分布往往不是对称的 ,偏度是客观存在的 ,而且投资者具有正偏度的爱好。所以必须用方差和偏度来共同度量投资的风险 ,在这种情况下 ,贝塔系数不再是风险的正确度量 ,采用有效的修正方法 ,可以用来对资产进行正确的定价     

Estimating the connectedness of commodity futures using a network approach

Using a network approach of variance decompositions, we measure the connectedness of 18 commodity futures and characterize both static and dynamic connectedness. Our results show that metal futures are net transmitters of shocks to other futures, and agricultural futures are vulnerable to shocks from the others. Furthermore, almost two-thirds of the volatility uncertainty for commodity futures are due to the connectedness of shocks across the futures market. Dynamically, we find connectedness always increases in times of turmoil. An analysis of connectedness networks suggests that investors could be forewarned that the connectedness of various classes of futures could threaten their portfolios.     

Mean–variance hedging of contingent claims with random maturity

We study the mean–variance hedging of an American-type contingent claim that is exercised at a random time in a Markovian setting. This problem is motivated by applications in the areas of employee stock option valuation, credit risk, or equity-linked life insurance policies with an underlying risky asset value guarantee. Our analysis is based on dynamic programming and uses PDE techniques. In particular, we prove that the complete solution to the problem can be expressed in terms of the solution to a system of one quasi-linear parabolic PDE and two linear parabolic PDEs. Using a suitable iterative scheme involving linear parabolic PDEs and Schauder's interior estimates for parabolic PDEs, we show that each of these PDEs has a classical C^{1, 2} solution. Using these results, we express the claim's mean–variance hedging value that we derive as its expected discounted payoff with respect to an equivalent martingale measure that does not coincide with the minimal martingale measure, which, in the context that we consider, identifies with the minimum entropy martingale measure as well as the variance-optimal martingale measure. Furthermore, we present a numerical study that illustrates aspects of our theoretical results.     

Volatility forecasts embedded in the prices of crude-oil options

This paper evaluates the ability of alternative option-implied volatility measures to forecast crude-oil return volatility. We find that a corridor implied volatility measure that aggregates information from a narrow range of option contracts consistently outperforms forecasts obtained by the popular Black–Scholes and model-free volatility expectations, as well as those generated by a realized volatility model. This measure ranks favorably in regression-based tests, delivers the lowest forecast errors under different loss functions, and generates economically significant gains in volatility timing exercises. Our results also show that the Chicago Board Options Exchange's “oil-VIX” index performs poorly, as it routinely produces the least accurate forecasts.     

基于有界协整方法的中国进口需求弹性研究

有界检验是由Pesaran等(2001)新提出的一种协整分析方法,本文利用这一方法对改革开放以来中国进口贸易与其决定因素之间的长期关系和需求弹性进行了分析。结果表明,无论是长期还是短期,中国的进口需求相对于价格缺乏弹性,但相对于收入具有较高的弹性。这一结论具有重要的政策含义:其一,某些国家力图通过促使人民币升值来缓解其贸易赤字的做法是缺乏论据支持的;其二,中国经济的增长是世界经济的积极贡献因素。     

The log-moment formula for implied volatility

We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that in the absence of arbitrage, if the underlying stock price at time T admits finite log-moments $\mathbb{E}[|\log S_T{|}^q]$ for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile for T is less constrained than Lee's bound. The result is rationalized by a market trading discretely monitored variance swaps wherein the payoff is a function of squared log-returns, and requires no assumption for the underlying price to admit any negative moment. In this respect, the result can be derived from a model-independent setup. As a byproduct, we relax the moment assumptions on the stock price to provide a new proof of the notorious Gatheral–Fukasawa formula expressing variance swaps in terms of the implied volatility.     

MULTI‐ASSET STOCHASTIC LOCAL VARIANCE CONTRACTS

Variance swaps now trade actively over‐the‐counter (OTC) on both stocks and stock indices. Also trading OTC are variations on variance swaps which localize the payoff in time, in the underlying asset price, or both. Given that the price of the underlying asset evolves continuously over time, it is well known that there exists a semirobust hedge for these localized variance contracts. Remarkably, the hedge succeeds even though the stochastic process describing the instantaneous variance is never specified. In this paper, we present a generalization of these results to the case of two or more underlying assets.     

浅析贷款风险的防范与化解

目前我国银行存在贷款风险隐患 ,解决贷款风险的根本出路在于深化改革 ,建立起符合市场经济要求的银企关系、信用体系、法制体系和培养一支高素质的金融队伍。由体制转型带来的贷款风险问题 ,将随着市场经济和金融事业的进一步发展而得到根本解决。     

论企业财务风险识别与测量

企业财务风险的识别与分析是企业财务风险防范的首要环节。通过正确地判断和发现企业面临的筹资风险、投资风险、资金回收风险等各种财务风险,确定财务风险发生的概率及损失程度．才能为风险的防范提供有意义的证据和做出正确及时的决策。     

我国开放式基金风险管理研究

开放式基金作为一种金融工具,其健康发展离不开对风险的有效管理和控制。本文详细分析了我国开放式基金所面临的各种风险,并提出了防范和管理开放式基金风险的建议和措施。与现有文献相比,本文提出了系统的开放式基金风险管理措施,并构建了开放式基金风险管理模型,形成了我国开放式基金风险管理系统,完善了开放式基金风险管理理论。