This study reconsiders the timing of the equity risk factors by using the flexible neural networks specified for image recognition to determine the timing weights. The performance of each factor is visualized to be standardized price and volatility charts and `learned' by flexible image recognition methods with timing weights as outputs. The performance of all groups of factors can be significantly improved by using these ``deep learning--based'' timing weights. In addition, visualizing the volatility of factors and using deep learning methods to predict volatility can significantly improve the performance of the volatility-managed portfolio for most categories of factors. Our further investigation reveals that the timing success of our method hinges on its ability in identifying ex ante regime switches such as jumps and crashes of the factors and its predictability on future macroeconomic risk.

This paper proposes the two-component realized EGARCH model with dynamic jump intensity (hereafter REGARCH-C-DJI model) to model and forecast stock market volatility. The key feature of our REGARCH-C-DJI model is its ability to exploit the high-frequency information as well as to capture the long memory volatility and jump dynamics. An empirical application to Shanghai Stock Exchange Composite (SSEC) index data shows the presence of high persistence of volatility and dynamic jumps in China’s stock market. More importantly, the REGARCH-C-DJI model dominates the GARCH, EGARCH, REGARCH and REGARCH-C models in terms of out-of-sample forecast performance. Our findings highlight the importance of accommodating the realized volatility, volatility components and jump dynamics in forecasting stock market volatility.

Using the regression discontinuity design, a quasi-experiment approach, this paper establishes a causal relationship between the down payment requirement and house prices by exploiting a unique institutional background in Shanghai. In the unique setting, the required minimal down payment ratio jumps at the Inner Ring, a circular elevated highway, from 50% to 70% for a large group of buyers. With transaction level data from the largest real estate broker in Shanghai, we find that a lower required down payment ratio increases the apartment price by 138.8 thousand RMB, around 3.71% of the average transaction price.

This paper investigates the intertemporal relation between expected aggregate stock market returns and conditional variance considering periodic trading breaks. We propose a modified version of Merton’s intertemporal asset pricing model that merges two different processes driving asset prices, (i) a continuous process modeling diffusive risk during the trading day and, (ii) a discontinuous process modeling overnight price changes of random magnitude. Relying on high-frequency data, we estimate distinct premia for diffusive trading volatility and volatility induced by overnight jumps. While diffusive trading volatility plays a minor role in explaining the expected market risk premium, overnight jumps carry a significant risk premium and establish a positive risk-return trade-off. Our study thereby contributes to the ongoing debate on the sign of the intertemporal risk-return relation.

This paper studies the magnet effect of market-wide circuit breakers and examines its possible forms using high-frequency data from the Chinese stock index futures market. Unlike previous studies that mainly analyzed the price trend and volatility, this paper is the first to consider the intraday price jump behavior in studying the magnet effect. We find that when a market-wide trading halt is imminent, the probability of a price decrease and the level of market volatility remain stable. However, the conditional probability of observing a price jump increases significantly, leading to a higher possibility of triggering market-wide circuit breakers, which is in support of the magnet effect hypothesis. In addition, we find a significant increase in liquidity demand and insignificant change in liquidity supply ahead of a market-wide trading halt, suggesting that the deterioration of market liquidity may play an important role in explaining the magnet effect.

It has been long that literature in finance focuses mainly on price and return but much less on trading volume, even completely ignoring it. There is no information on supply-demand quantity and trading volume in neoclassical finance models. Contrary to one of the clearest predictions of rational models of investment in a neoclassical paradigm, however, trading volume is very high on the world’s stock market. Here we extend Shi’s price-volume differential equation, propose a notion of trading conditioning, and measure the intensity of market crowd trading conditioning by accumulative trading volume probability in the wave equation in terms of classical and operant conditioning in behavior analysis. Then, we develop three kinds of market crowd trading behavior models according to the equation, and test them using high frequency data in China stock market. It is hardly surprising that we find: 1) market crowd behave coherence in interaction widely and reach agreement on a stationary equilibrium price between momentum and reversal traders; 2) market crowd adapt to stationary equilibrium price by volume probability increase or decrease in interaction between market crowd and environment (or information and events) in an open feedback loop, and keep coherence by conversion between the two types of traders when it jumps and results in an expected return from time to time, the outcome of prior trading action; 3) while significant herd and disposition “anomalies” disappear simultaneously by learning experience in a certain circumstance, other behavioral “anomalies”, for examples, greed and panic, pronounce significantly in decision making. Specifically, a contingency of return reinforcement and punishment, which includes a variety of internal and external causes, produces excessive trading volume. The behavioral annotation on the volume probability suggests key links and the new methods of mathematical finance for quantitative behavioral finance.长期以来，金融的学术文献主要关注价格和回报率，很少考虑甚至完全忽视了交易量。新经典金融模型就没有供需量和交易量的信息。然而，与新经典框架理性投资模型的预计结果不同，交易量在世界的股票市场上是非常大的。我们基于Shi的价-量微分方程，根据行为分析中的经典性和操作性条件反射，提出了交易性条件反射的概念，并且用该方程中的累计交易量概率来计量市场群体交易性条件反射的强度。由该方程，我们得到三种市场群体的交易行为模型，并且用我国股市的高频数据进行实证分析。不难发现：1）市场群体在相互作用的过程中普遍地表现出相互一致的行为特征，趋势和反转交易者之间存在着一个大家都能够接受的稳态均衡价格；2）交易行为有时会导致稳态均衡价格出现跳跃、带来预期收益率，这时，市场群体在开放的反馈环中，通过与环境（或信息和事件）之间的相互作用，由成交量概率的增加或减少来适应该均衡价格的变化，趋势和反转交易者也会通过相互转换保持市场群体行为的相互一致性； 3）尽管在某特定环境下市场群体通过学习实践，羊群和处置行为同时消失了，但是其他行为“异象”，例如贪婪与恐慌，在决策中却表现的十分显著。特别地，收益率强化和惩罚过程，其中包含各种内外因素，导致过度交易量。累计交易量概率的行为诠释为计量行为金融学提供了关键性的纽带作用和数学金融的新方法。

This paper studies idiosyncratic risk of new ventures. An option-based model of a new venture with multistage investments and jumps is developed. Our model ex- plains (1) why new ventures?idiosyncratic volatility eventually decreases as they clear R&D investment stages and become mature ?rms ?the stage-clearing e¤ect; (2) the negative relation between jumps in value and subsequent idiosyncratic volatility ?the jump e¤ect; (3) the dynamics of idiosyncratic volatility under di¤erent schedules of staged venture capital investments; and (4) the e¤ect of di¤erent schedules of staged investments on ?rm valuation with the presence of jumps. Empirically, we develop a generalized Markov-Switching EARCH model to simultaneously capture structural changes in ?rms?idiosyncratic volatility and the relation between jumps and idiosyn- cratic volatility. Using a hand-collected dataset of early-stage biotech ?rms, we ?nd empirical evidence supporting the jump e¤ect and the stage-clearing e¤ect described by our model.

Early-stage ?rms usually have a single large Research and Development (R&D) project that requires multi-stage investment. Firms? volatility can dramatically change due to the evolvement of R&D e¤orts and stage clearing. First, the success (failure) of R&D e¤orts within each stage (jump risk) decreases (increases) the un- certainty (i.e. volatility) level of the ?rms?future returns ?"jump e¤ect". Second, at the end of each stage, ?rms decide whether to continue next stage investment upon re-evaluating the project prospect conditional on the resolution of technical uncertainty and other information; as ?rms survive each investment stage and are becoming mature, the uncertainty level of their future returns should eventually decrease in later investment stages that lead to maturity ?"stage-clearing e¤ect". Ignoring these e¤ects results in incorrect estimation of ?rms?future volatility, an important element for early-stage ?rm valuation. In this paper, I develop a gener- alized Markov-Switching EARCH methodology for early-stage ?rms with discrete stage-clearing and jumps. My methodology can identify structural changes in the idiosyncratic volatility and also explore the relation between price changes and future volatility. Using a hand-collected dataset of early-stage biotech ?rms, I con?rmed the existence of the "stage-clearing e¤ect" and the "jump e¤ect". In the second part of my paper, I model early-stage ?rms as sequences of nested call options with jumps that lead to mature ?rms. "Jump e¤ect" arises because the early-stage ?rms are modeled as compound call options with jumps on the underly- ing cash ?ows, the volatility of the early-stage ?rms at each stage is determined by the compound call option elasticity to the underlying cash ?ows. If the downside (upside) jump happens, the value of the underlying cash ?ows decreases (increases), which makes the compound call option elasticity go up (down). As a result, the compound call option becomes riskier (less risky). "Stage-clearing e¤ect" arises because as ?rms exercise their option to continue investment, the new options that ?rms enter into will eventually become a less risky option.

This paper studies sequential portfolio choices by MPS-risk-averse investors in a continuous time jump-diffusion framework. It is shown that the optimal trading strategies for MPS risk averse investors, if they exist, must be located on a so-called `temporal efficient frontier' (t.e.f.). The t.e.f. is found not to coincide with the local instantaneous frontier --- the continuous time analogue of Markowitz's mean-variance frontier. This observation is potentially useful in understanding the existence of documented financial anormally in empirical finance --- MPS risk averse investors may not wish to invest along the local instantaneous Markowitz's mean-variance frontier, but instead hold portfolios on the t.e.f.. The optimal portfolio on the t.e.f. could well fall strictly within the instantaneous local Markowitz's efficient frontier. Our observations on mutual fund separation are also profound and interesting. In contrast to the classical two-fund separation along the line of Black (1972) and Tobin (1958), our study shows that MPS-risk-averse investors' optimal trading strategy is target rate specific. Precisely, investors with different target rates may end up investing into different managed mutual funds, each involving a specific set of separating portfolios. Our theoretic findings are, nevertheless, much in line with the real world phenomena on the existence of various types of mutual funds offered by different financial institutes, each aiming to attract demand from some specific groups of investors --- a picture that is in sharp contrast to the theoretical prediction made by Black (1972) and Tobin (1958). Finally, our study sheds light on the difference between expected utility and MPS-risk-averse investors concerning their trading behavior in sequential time frame. Even though these two groups of investors may end up holding a common risky portfolio in each spot market, the differences between their trading behaviors are most reflected through the portfolio weights assigned to each of the separating portfolios within the time frame and across states. Precisely, the portfolio weights corresponding to investors respectively from the two groups are associated with recognizable different time patterns. We showed that such difference in trading behavior would be also reflected from the time patterns of the instantaneous returns and the volatilities of the funds respectively managed by investors from these two groups.

We provide a comprehensive analysis of the out-of-sample performance of a wide variety of spot rate models in forecasting the probability density of future interest rates. While the most parsimonious models perform best in forecasting the conditional mean of many financial time series, we find that the spot rate models that incorporate conditional heteroskedasticity and excess kurtosis or heavy-tails have better density forecasts. GARCH significantly improves the modeling of the conditional variance and kurtosis, while regime switching and jumps improve the modeling of the marginal density of interest rates. Our analysis shows that the sophisticated spot rate models in the existing literature are important for applications involving density forecasts of interest rates.