News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns

This paper models components of the return distribution, which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. A heterogeneous Poisson process with a time‐varying conditional intensity parameter governs the likelihood of jumps. Unlike typical jump models with stochastic volatility, previous realizations of both jump and normal innovations can feed back asymmetrically into expected volatility. This model improves forecasts of volatility, particularly after large changes in stock returns. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, leverage effects, and the time‐series dynamics of jump clustering.     

上证指数收益率波动的实证分析：基于ARCH族模型

股价指数的收益率序列具有时变波动性、厚尾特征、波动性群集等特点,传统的计量分析无法刻画这些特点。文章利用ARCH族模型,选取2003年1月20日～2013年12月12日上证指数每日收益率共2621个数据对其波动进行定量与定性的分析,结果显示,上证指数日收益率存在高阶的ARCH效应,杠杆效应,波动集聚性特征,条件方差对日收益率有很强的影响,其中EGARCH模型在反映股市波动性方面优于其他模型。     

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

Samuelson Hypothesis & Indian Commodity Derivatives Market

Samuelson (1965) devised that futures price volatility increases as the futures contract approaches its expiration. The relation amid the volatility and time to maturity has significant inference for hedging strategies. Interestingly, so far the empirical evidence in favor of the Samuelson Hypothesis (maturity effect) is mixed in various markets. Considering no significant work to examine the relationship is so far carried out in commodity derivative markets of India, this paper ordeal the Samuelson Hypothesis on 8 commodities traded on Multi-Commodity Exchange (MCX), India. We have examined the issue by applying different regression techniques to test the hypothesis for 8 commodities (Aluminium, Nickel, Copper, Gold, Silver, Natural Gas, Crude Oil and Wheat) using inter-day data on MCX India. In order to test the Samuelson’s hypothesis, tests have been conducted using a series of GARCH, EGARCH and TGARCH models by including trading volume, open interest and time-to-maturity in the conditional variance equation. From our results, it is concluded that Samuelson’s hypothesis does not hold true for majority of commodity contracts considered. Our results also find that volatility series depend on the trading volume, compared to the time-to-maturity or open interest. As Samuelson hypothesis does not hold true for majority of commodity contracts, traders in Indian commodity derivative markets should not bias their decisions solely based on the time-to-maturity, but should also consider trading volume and open interest as they are an important determinant of price volatility. They should also consider the possibility of leverage effect while predicting future price volatilities, and the associated margin requirements.     

Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

Forecasting variance using stochastic volatility and GARCH

This paper estimates the conditional variance of daily Swedish OMX-index returns with stochastic volatility (SV) models and GARCH models and evaluates the in-sample performance as well as the out-of-sample forecasting ability of the models. Asymmetric as well as weekend/holiday effects are allowed for in the variance, and the assumption that errors are Gaussian is released. Evidence is found of a leverage effect and of higher variance during weekends. In both in-sample and out-of-sample comparisons SV models outperform GARCH models. However, while asymmetry, weekend/holiday effects and non-Gaussian errors are important for the in-sample fit, it is found that these factors do not contribute to enhancing the forecasting ability of the SV models.     

Announcement Effects and Asymmetric Volatility in Industry Stock Returns: Evidence from Taiwan

This study employs financial econometric models to examine the asymmetric volatility of equity returns in response to monetary policy announcements in the Taiwanese stock market. The meetings of the board of directors at the Central Bank of the Republic of China (Taiwan) are considered for testing the announcement effects. The asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) model and the smooth transition autoregression with GARCH model are used to measure equity returns' asymmetric volatility. We conclude that the asymmetric volatility of countercyclical equity returns can be identified. Our findings support the leverage effect of stock price changes for most industry equity returns in Taiwan.     

Optimal delta hedging for options

As has been pointed out by a number of researchers, the normally calculated delta does not minimize the variance of changes in the value of a trader's position. This is because there is a non-zero correlation between movements in the price of the underlying asset and movements in the asset's volatility. The minimum variance delta takes account of both price changes and the expected change in volatility conditional on a price change. This paper determines empirically a model for the minimum variance delta. We test the model using data on options on the S&P 500 and show that it is an improvement over stochastic volatility models, even when the latter are calibrated afresh each day for each option maturity. We also present results for options on the S&P 100, the Dow Jones, individual stocks, and commodity and interest-rate ETFs.     

Stochastic volatility and stochastic leverage

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new models. Furthermore, we give a detailed account on statistical properties of the new models.     

融资融券交易对市场和标的个股波动影响的研究

作为证券市场的重要制度之一,融资融券交易理论上应具有价格发现,价格稳定,提高流动性等基本功能。本文从融资、融券交易对市场和个股两个层面系统而全面的分析融资交易和融券交易的价格稳定作用。对市场波动性的影响的研究上主要借助GARCH族模型,VAR模型,脉冲响应和方差分解等计量分析方法;在对个股的影响上主要是借助面板数据分对个股的总体效应和个体效应展开分析。研究发现：融资交易对指数波动没有显著影响,融券交易对指数波动有一定平抑作用;融资融券交易对标的个股有价格稳定作用,除极个别个股的融资作用表现不确定。     

The leverage effect puzzle: the case of European sovereign credit default swap market

One of the stylized facts about the behaviour of time series is that their volatility exhibits asymmetrical responses to good and bad news. In the case of stock markets, volatility seems to rise when the stock price decreases and fall when the stock price increases. This so-called “leverage effect” was first described by Black (Proceedings of the 1976 meeting of the business and economic statistics section, pp 177–181, 1976). The concept is not new and has already been comprehensively studied and implemented in many volatility models (GARCH and SV) in the form of an additional parameter in the volatility equation. However, there is no study or a theoretical explanation of the leverage effect in sovereign credit default swap spreads (hereinafter: sCDS). In this article, we discuss the possible behaviour of sCDS volatility and explain it by way of reference to the Prospect Theory by Kahneman and Tversky (Econometrica 47(2):263–292, 1979). We estimate a series of stochastic volatility models with the leverage effect, proposed by Yu (J Econom 127(2):165–178, 2005). In this model, the “leverage effect” is, in fact, the same as a coefficient of the correlation between the current return of an asset and its expected future volatility. We show that the effect does exist and differs across markets. As far as the safe European markets are concerned, the parameter is negative; in the case of extremely risky economies—it is positive. In markets of medium risk the effect varies depending on the relationship between the perceived risk and the value of the sCDS premium.     

Stock Price Dynamics and Firm Size: An Empirical investigation

We show that after controlling for the effects of bid-ask spreads and trading volume the conditional future volatility of equity returns is negatively related to the level of stock price. This “leverage effect” is stronger for small, as compared to large, firms. We also document that while the essential characteristics of the relations between stock price dynamics and firm size are stable, the strengths of the relationships appear to change over time.     

Pricing under rough volatility

From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated variance. We analyse in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.     

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.     

Stock market liberalization and return volatility: Evidence from the emerging market of Sri Lanka

This study examines the impact of liberalization of the Sri Lankan stock market on return volatility. We specify GARCH and TGARCH models of volatility, and estimate them using 16 years of weekly returns for the period from 1985 to 2000. The results show that liberalization of the market to foreign investors significantly increased the return volatility in the Colombo Stock Exchange. Both conditional and unconditional volatility measures are the highest in the liberalization period. Negative return shocks lead to lower volatility suggesting that there is no leverage effect, and this appears to reflect the very low levels of leverage used by Sri Lankan companies.     

Conditional Dependence in Precious Metal Prices

This study investigates the time-series properties of gold and silver spot prices. Both precious metal price series are found to exhibit time dependence and pronounced generalized autoregressive conditional heteroscedastic (GARCH) effects. Splitting the data into similar economic subperiods provides superior explanation of these effects because of the observed long-run nonconstancy of the unconditional variance. Further, the power exponential distribution, as opposed to the Student-t, is found to portray accurately the thick-tailed conditional variance that remains after the GARCH effects are removed. These findings imply that constant variance pricing models are inappropriate for securities that are based on precious metal prices.     

Short-term Dynamics in the Cyprus Stock Exchange

Abstract

This paper investigates the short-term dynamics of stock returns in an emerging stock market namely, the Cyprus Stock Exchange (CYSE). Stock returns are modelled as conditionally heteroscedastic processes with time-dependent serial correlation. The conditional variance follows an EGARCH process, while for the conditional mean three nonlinear specifications are tested, namely: (a) the LeBaron exponential autoregressive model; (b) the Sentana and Wadhwani positive feedback trading model; and finally (c) a model that nests both (a) and (b). There is an inverse relationship between volatility and autocorrelation consistent with the findings from several other stock markets, including the US. This pattern could be the manifestation of a certain form of noise trading namely positive feedback trading or, momentum trading strategies. There is little evidence that market declines are followed with higher volatility than market advances, the so-called ‘leverage effect’, that has been observed in almost all developed stock markets. In out of sample forecasts, the nonlinear specifications provide better results in terms of forecasting both first and second moments of the distribution of returns.     

New Evidence on Sources of Leverage Effects in Individual Stocks

I test Black's leverage effect hypothesis on a panel of U.S. stocks from 1997 to 2012. I find that negative stock return innovations increase the future volatility of equity returns by about 36% more than positive ones. There is a strong and positive relation between variation in the size of these leverage effects and variation in the firm's use of debt. I uncover this relation by applying the Fama/French/Carhart 4‐factor asset pricing model in the exponential generalized autoregressive conditional heteroskedasticity mean equation and by using panel data to control for firm‐ and time‐invariant unobservables via first differences and two‐way fixed effects.     

Leverage causes fat tails and clustered volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called ‘value investing’, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage, i.e. borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times, funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds is fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset, this can cause substantial losses. This in turn leads to clustered volatility: before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power-law tails, which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on ‘irrational behavior’, such as trend following. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility becomes high, making these extreme fluctuations even worse.