Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe theory on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of US stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behaviour in the second half. Translating the results, we find that the US stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.     

金融市场MAX效应的影响因素研究 ——基于价格视角

金融市场的变量虽然纷繁复杂,但价格因其直观性和重要性,成为金融市场参与者最易观察且难以忽略的变量,正因如此,价格对市场参与者的心理和行为产生了深刻影响.以中国股市2004年1月至2020年6月的数据为样本,探究价格因素会如何影响由追涨行为所导致的M AX效应.实证结果发现:投资者的追涨勇气和热情明显会受到价格影响,即当反应市场整体价格水平的股指指数近期上涨或波动率越小时,亦或当个股价格越低于其前期最高价、越低于投资者购买价时,投资者越乐于追涨具有"高极端收益"的个股,M AX效应也随之会更显著.     

Market impact: a systematic study of the high frequency options market

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders—large orders that are split into smaller pieces before being sent to the market—on one of the main Asian markets. In line with our previous work on the equity market [Said, E., Bel Hadj Ayed, A., Husson, A. and Abergel, F., Market impact: A systematic study of limit orders. Mark. Microstruct. Liq., 2018, 3(3&4), 1850008.], we propose an algorithmic approach to identify metaorders, based on some implied volatility parameters, the at the money forward volatility and at the money forward skew. In both cases, we obtain results similar to the now well-understood equity market: Square-Root Law, Fair Pricing Condition and Market Impact Dynamics.     

Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

24-Hour realized volatilities and transatlantic volatility interdependence

This paper proposes an innovative econometric approach for the computation of 24-h realized volatilities across stock markets in Europe and the US. In particular, we deal with the problem of non-synchronous trading hours and intermittent high-frequency data during overnight non-trading periods. Using high-frequency data for the Euro Stoxx 50 and the S&P 500 Index between 2003 and 2011, we combine squared overnight returns and realized daytime variances to obtain synchronous 24-h realized volatilities for both markets. Specifically, we use a piece-wise weighting procedure for daytime and overnight information to take into account structural breaks in the relation between the two. To demonstrate the new possibilities that our approach opens up, we use the new 24-h volatilities to estimate a bivariate extension of Corsi et al.’s [Econom. Rev., 2008, 27(1–3), 46–78] HAR-GARCH model. The results suggest that the contemporaneous transatlantic volatility interdependence is remarkably stable over the sample period.     

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.     

The shape of small sample biases in pricing kernel estimations

Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kernels typically violate the commonly believed monotonicity at the centre even when the true pricing kernel fulfils these. This contributes to an alternative, statistical explanation for the puzzling shape in pricing kernel estimations.     

Determining the integrated volatility via limit order books with multiple records

The integrated volatility plays an important role in risk management and portfolio selection, the estimation methods regarding the quantity have been widely investigated, either under low-frequency data or high-frequency data, or a combination of both. In this paper, we propose a measure for the integrated volatility via limit order book data with possible presence of multiple records. The estimator is valid under mild conditions and it is easily implemented. The finite sample performance of the proposed estimator has been verified by simulation studies and we apply the method to some real high-frequency data-sets as well.     

Risk–Return Profiles of Islamic Equities and Commodity Portfolios in Different Market Conditions

Motivated by the recent phenomenal growth in Islamic finance and the financialization of commodities, this study makes an initial attempt to investigate the risk–return profiles of optimized portfolios combining (a) Islamic equities with commodities and (b) conventional equities with commodities during the crises and noncrises periods. The findings tend to indicate that Islamic equity–commodity portfolios provide relatively higher diversification benefits than the conventional equity–commodity portfolios during the 1997 Asian Financial Crisis triggered by the financial sector compared to the 2008 global financial crisis triggered by the real housing sector. The findings further suggest that except for a few cases, commodities in general and gold in particular improve diversification benefits.     

Political uncertainty and a firm's credit risk: Evidence from the international CDS market

Using a large sample of firms with single-name credit default swap (CDS) contracts in 30 countries, we document the evidence that political uncertainty, proxied by national election dummy, is positively related to firm-level credit risk. Specifically, this positive relation is more pronounced for the firms that have no political connection or poor international diversification, and in the countries with higher political uncertainty and lower investor protections. Further, by using a difference-in-differences approach, we find evidence to support idiosyncratic volatility and debt rollover channels through which political uncertainty affects the credit risk of individual firm.