Jumping Risk Communities in the Energy Industry: An Empirical Analysis Based on Time-Varying Complex Networks

This paper uses the 5-five-minute high-frequency data of energy-listed companies in China's A-share market to extract the jump of energy stock prices and build a dynamic stock price jump complex network. Then, we analyze the clustering effect of the complex network. The research shows that the energy stock price jump is an important part of stock price volatility, and the complex network of energy stock jump risk has obvious time-varying characteristics. However, the infection problem of stock price jump risks needs specific analysis. China's coal industry has an important influence on the development of China's energy industry. According to the clustering analysis results of the network community, the clustering effect of the network community has time-varying characteristics. After October 2017, the clustering effect of the jumping risk of the coal industry and the new energy industry is obvious. The risk contagion within the new energy industry community is a key point for the development of the new energy industry.

Equity Option Pricing with Systematic and Idiosyncratic Volatility and Jump Risks

Recently, a large number of empirical studies indicated that individual equity options exhibit a strong factor structure. In this paper, the importance of systematic and idiosyncratic volatility and jump risks on individual equity option pricing is analyzed. First, we propose a new factor structure model for pricing the individual equity options with stochastic volatility and jumps, which takes into account four types of risks, i.e., the systematic diffusion, the idiosyncratic diffusion, the systematic jump, and the idiosyncratic jump. Second, we derive the closed-form solutions for the prices of both the market index and individual equity options by utilizing the Fourier inversion. Finally, empirical studies are carried out to show the superiority of our model based on the S&P 500 index and the stock of Apple Inc. on options. The out-of-sample pricing performance of our proposed model outperforms the other three benchmark models especially for short term and deep out-of-the-money options.

EQUILIBRIUM PRICE OF VARIANCE SWAPS UNDER STOCHASTIC VOLATILITY WITH LÉVY JUMPS AND STOCHASTIC INTEREST RATE

This paper focuses on the pricing of variance swaps in incomplete markets where the short rate of interest is determined by a Cox–Ingersoll–Ross model and the stock price is determined by a Heston model with simultaneous Lévy jumps. We obtain the pricing kernel and the equivalent martingale measure in an equilibrium framework. We also give new closed-form solutions for the delivery prices of discretely sampled variance swaps under the forward measure, as opposed to the risk neural measure, by employing the joint moment generating function of underlying processes. Theoretical results and numerical examples are provided to illustrate how the values of variance swaps depend on the jump risks and stochastic interest rate.

An Empirical Analysis of Bitcoin Price Jump Risk

Given that there are both continuous and discontinuous components in the movement of asset prices, existing asset pricing models that assume only continuous price movements should be revised. In this paper, we explore the features of jumps, which are discontinuous movements, by examining Bitcoin pricing. First, we identify jumps in the Bitcoin price on a daily basis, applying a non-parametric methodology and then break down the Bitcoin total rate of return into a jump rate of return and a continuous rate of return. In our empirical analysis, price jumps turn out to be independent of volatility. Moreover, the jumps in the Bitcoin price do not appear at regular intervals; rather, they tend to be concentrated in clusters during special periods, implying that once an economic crisis occurs, the crisis will last for a long time due to contagion effects and the economy will take a considerable amount of time to recover fully. Further, the contribution of the jump rate of return to the total rate of return of the Bitcoin price is lower than the contribution of the continuous return, implying that the pursuit of sustainable returns rather than large but temporary returns will improve the total rate of return over the long term. Finally, more jumps are observed when trading volume is lower, implying that market illiquidity drives discontinuous movement in asset prices. Overall, the features of jump risk are like two sides of the same coin and jump risks are expected to have a significant effect on asset pricing, suggesting that consideration of jumps is essential for risk management as well as asset pricing.

Measuring Tail Risks at High Frequency

I exploit information in the cross-section of bid-ask spreads to develop a new measure of extreme event risk. Spreads embed tail risk information because liquidity providers require compensation for the possibility of sharp changes in asset values. I show that simple regressions relating spreads and trading volume to factor betas recover this information and deliver high-frequency tail risk estimates for common factors in stock returns. My methodology disentangles financial and aggregate market risks during the 2007–2008 financial crisis; quantifies jump risks associated with Federal Open Market Committee announcements; and anticipates an extreme liquidity shock before the 2010 Flash Crash. Received April 27, 2016; editorial decision August 10, 2018 by Editor Andrew Karolyi. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online