A note on the Wang and Wang measure of the quality of the compass rose

H. Wang and C. Wang [Visibility of the compass rose in financial asset returns: A quantitative study, J. Bank. Financ. 26 (2002), 1099–1111] derive a measure of the visibility of the radial patterns that appear in a plot of current and past returns, which are more commonly known as the compass rose. In theory, this measure should be positively related to the tick/volatility ratio. In practice however, we find that this relationship does not hold for higher tick/volatility ratios that are common to stock market data. Thus, the use of this measure is limited in real world applications. We propose a correction factor that improves the behaviour of the quality measure over higher tick/volatility ratios, however, further research is required to fully identify and correct the problem.     

Robust Structure Without Predictability: The “Compass Rose” Pattern of the Stock Market

Plotting daily stock returns against themselves with one day's lag reveals a striking pattern. Evenly spaced lines radiate from the origin; the thickest lines point in the major directions of the compass. This “compass rose” pattern appears in every stock. It is caused by discreteness. However, counter-examples demonstrate that the existence of exchange-imposed tick sizes (e.g. eighths) is neither necessary nor sufficient for the compass rose. The compass rose cannot be used to make abnormal profits: it is structure without predictability. Among other consequences, the compass rose may bias estimation of ARCH models, and tests for chaos.     

Price dynamics in refined petroleum spot and futures markets

This article characterizes the spot and futures price dynamics of two important physical commodities, gasoline and heating oil. Using a non-linear error correction model with time-varying volatility, we demonstrate many new results. Specifically, the convergence of spot and futures prices is asymmetric, non-linear, and volatility inducing. Moreover, spreads between spot and futures prices explain virtually all spot return volatility innovations for these two commodities, and spot returns are more volatile when spot prices exceed futures prices than when the reverse is true. Furthermore, there are volatility spillovers from futures to spot markets (but not the reverse), futures volatility shocks are more persistent than spot volatility shocks, and the convergence of spot and futures prices is asymmetric and non-linear. These results have important implications. In particular, since the theory of storage implies that spreasd vary with fundamental supply and demand factors, the strong relation between spreads and volatility suggests that these fundamentals — rather than trading induced noise — are the primary determinants of spot price volatility. The volatility spillovers, differences in volatility persistence, and lead-lag relations are consistent with the view that the futures market is the primary locus of informed trading in refined petroleum product markets. Finally, our finding that error correction processes may be non-linear, asymmetric, and volatility inducing suggests that traditional approaches to the study of time series dynamics of variables that follow a common stochastic trend that ignore these complexities may be mis-specified.     

Oil Futures Prices in a Production Economy with Investment Constraints

We document a new stylized fact, that the relationship between the volatility of oil futures prices and the slope of the forward curve is nonmonotone and has a V-shape. This pattern cannot be generated by standard models that emphasize storage. We develop an equilibrium model of oil production in which investment is irreversible and capacity constrained. Investment constraints affect firms' investment decisions and imply that the supply elasticity changes over time. Since demand shocks must be absorbed by changes in prices or changes in supply, time-varying supply elasticity results in time-varying volatility of futures prices. Estimating this model, we show it is quantitatively consistent with the V-shape relationship between the volatility of futures prices and the slope of the forward curve.     

Commodity volatility breaks

Volatility is a key determinant of derivative prices and optimal hedge ratios. This paper examines whether there are structural breaks in commodity spot return volatility using an iterative cumulative sum of squares procedure and then uses GARCH (1,1) to model volatility during each regime.The main empirical finding is the very limited evidence of commodity volatility breaks during the recent financial crisis. This suggests commodity return volatility was not exceptionally high during the recent financial crisis compared to the 1985–2010 sample period as a whole. For many commodities there are multiple idiosyncratic breaks in volatility; this suggests commodity specific supply or demand factors are important determinants of volatility. The empirical results overall are consistent with the view that commodities are too diverse to be considered as an asset class. Finally, we find commodity volatility persistence remains very high for many commodity returns even after structural breaks are accounted for.     

Forecasting value‐at‐risk in oil prices in the presence of volatility shifts

Recent evidence suggests shifts (structural breaks) in the volatility of returns causes non‐normality by significantly increasing kurtosis. In this paper, we endogenously detect significant shifts in the volatility of oil prices and incorporate this information to estimate Value‐at‐Risk (VaR) to accurately forecast large declines in oil prices. Our out‐of‐sample performance results indicate that the model, which incorporates both time varying volatility (without making any distributional assumptions) and shifts in volatility, produces more accurate VaR forecasts than several benchmark methods. We make a timely contribution as the recent more frequent occurrences of unexpected large oil price declines has gained significant attention because of its substantial impact on the financial markets and the global economy.     

Return and Volatility Spillovers Between Large and Small Stocks in the UK

Abstract:  This paper investigates return and volatility spillover effects between the FTSE 100, FTSE 250 and FTSE Small Cap equity indices using the multivariate GARCH framework. We find that return and volatility transmission mechanisms between large and small stocks in the UK are asymmetric. In particular, there are significant spillover effects in both returns and volatility from the portfolios of larger stocks to the portfolios of smaller stocks. For volatility, there is also evidence of limited feedback from the portfolios of smaller stocks to the portfolios of larger stocks, although sub-period analysis suggests that this is to some extent period-specific. Simulation evidence shows that non-synchronous trading potentially explains some, but not all, of the spillover effects in returns, and that it explains none of the spillover effects in volatility. These results are consistent with a market in which information is first incorporated into the prices of large stocks before being impounded into the prices of small stocks.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Does the Hurst index matter for option prices under fractional volatility?

This study examines the effect of fractional volatility on option prices. To this end, we develop an approximation method for the pricing of European-style contingent claims when volatility follows a fractional Brownian motion. Through extensive numerical experiments, we confirm that the decrease in the smile amplitude under fractional volatility is much slower than that under the standard stochastic volatility model. We also show that the Hurst index under fractional volatility has a crucial impact on option prices when the maturity is short and speed of mean reversion is slow. On the contrary, the impact of the Hurst index on option prices reduces for long-dated options.     

Retrieving risk neutral moments and expected quadratic variation from option prices

This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange.     

Implications of domestic price insulation for global food price behavior

Rapid changes in global food prices in recent years are widely viewed as a serious threat to global development. While various sources of price instability in agriculture have been identified, little attention appears to have been given to the importance of changes in trade policies that insulate domestic prices from world markets as a source of volatility in world prices. A contribution of this paper is to show that these interventions are dynamically more complex than simple proportional insulation. Insulation against an initial price increase in world prices increases the magnitude of that increase, while subsequent adjustments to the level of protection change the fundamental nature of price volatility. We find such policies are widespread and increase the volatility of world prices while not reducing the volatility of domestic prices because of the collective action problem involved in this form of policy intervention.     

How Do Investors' Expectations Drive Asset Prices?

Based on an extension of the process of investors' expectations to stochastic volatility we derive asset price processes in a general continuous time pricing kernel framework. Our analysis suggests that stochastic volatility of asset price processes results from the fact that investors do not know the risk of an asset and therefore the volatility of the process of their expectations is stochastic, too. Furthermore, our model is consistent with empirical studies reporting negative correlation between asset prices and their volatility as well as significant variations in the Sharpe ratio.     

Interest Rate Surprises and Stock Prices

This paper examines the impact of unexpected changes in the federal funds target on stock prices from 1988 to 2001. Measures of interest rate surprises are constructed from survey data and changes in the 3-month T-bill yield. I find that surprises associated with decreases in the target cause stock prices to rise significantly. Surprises associated with increases in the target increase stock market volatility on the announcement day, with volatility reverting to pre-surprise levels on the day after the announcement. This volatility pattern is only evident since 1994. An implication is that concerns about immediate disclosure causing persistent and heightened stock market volatility might be misplaced.     

Physical delivery versus cash settlement: an empirical study on the feeder cattle contract

This paper investigates the effects of the switch from physical delivery to cash settlement on the behavior of the cash and futures prices of the feeder cattle contract traded on the Chicago Mercantile Exchange. A bivariate Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is applied to estimate the conditional volatility structure, with a possible structural break due to the switch to cash settlement. The results show that the volatility of the futures prices (but not the cash prices) declined after physical delivery was replaced by cash settlement. In terms of futures hedging, cash settlement led to smaller and more stable hedge ratios. The variance of the hedged portfolio also decreased substantially. The evidence suggests that cash settlement is beneficial to the feeder cattle futures market.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

Validity of discrete-time stochastic volatility models in non-synchronous equity markets

The paper investigates the validity of versions of discrete-time stochastic volatility models for index series known to contain component stocks exhibiting non-synchronous trading. The efficient method of moments (EMM) is used to fit versions of the discrete-time stochastic volatility (SV) model. The EMM methodology confronts moment conditions generated by a score generator (SNP) that are valid by construction. The moment generator suggests non-linearity in the index series. The EMM construction shows that a classical discrete time stochastic volatility model is rejected. An extended model incorporating an asymmetric volatility specification validates all the moment scores. Option values from Black and Scholes (BS) and Monte Carlo simulations (MC) seem significantly different. The results suggest that BS does not price asymmetry adequately. Asymmetry suggests increased market risk inducing higher BS call prices and lower (higher) BS put pricing for ATM and OTM options (ITM) relative to MC.     

Detecting volatility persistence in GARCH models in the presence of the leverage effect

Most asset prices are subject to significant volatility. The arrival of new information is viewed as the main source of volatility. As new information is continually released, financial asset prices exhibit volatility persistence, which affects financial risk analysis and risk management strategies. This paper proposes a nonlinear regime-switching threshold generalized autoregressive conditional heteroskedasticity model which can be used to analyse financial data. The empirical results based on quasi-maximum likelihood estimation presented in this paper suggest that the proposed model is capable of extracting information about the sources of volatility persistence in the presence of the leverage effect.     

Information,interest rates,and the volatility of asset prices

The volatility of an asset price is modelled as a function of the volatility of an information signal, real interest rates and inflation expectations. Volatility depends on the duration of cash flows, and the degree to which cash flows are indexed to real rates and inflation. The model is applied to determine asset betas, the volatility of the futures prices of assets and the volatility of equity prices.     

Intraday and interday volatility in the Japanese stock market

This paper characterizes the volatility in the Japanese stock market based on a 4-year sample of 5-min Nikkei 225 returns from 1994 through 1997. The intradaily volatility exhibits a doubly U-shaped pattern associated with the opening and closing of the separate morning and afternoon trading sessions on the Tokyo Stock Exchange. This feature is consistent with market microstructure theories that emphasize the role of private and asymmetric information in the price formation process. Meanwhile, readily identifiable Japanese macroeconomic news announcements explain little of the day-to-day variation in the volatility, confirming previous findings for US equity markets. Furthermore, by appropriately filtering out the strong intradaily periodic pattern, the high-frequency returns reveal the existence of important long-memory interdaily volatility dependencies. This supports recent results stressing the importance of exploiting high-frequency intraday asset prices in the study of long-run volatility properties of asset returns.