10 - Multifrequency Jump-Diffusions

The specification of the stochastic process for stock prices is an important assumption underlying most equilibrium and option-pricing models in modern finance. This is particularly true of the continuous-time capital asset pricing models where it is assumed that asset prices follow diffusion processes with continuous sample paths (see Merton 1973a; Breeden 1979; Grossman and Shiller 1982). The extent to which the implications of these models generalize to discontinuous sample paths is an unanswered question in theoretical finance. However, the answer to this question is of more than just theoretical interest since accumulated empirical evidence appears to be inconsistent with the continuous sample path assumption (see Rosenberg 1972; Oldfield, Rogalski, and Jarrow 1977; Rosenfeld 1982). One purpose of this paper is to provide some answers to this question. We do this by extending Merton's (1973a) intertemporal asset pricing model, in the special case of a constant investment opportunity set, to include discontinuous sample paths for asset prices. The constant investment opportunity set assumption is imposed because we are interested in obtaining sufficient conditions under which an instantaneous capital asset pricing model (CAPM) results. The extension of our model to a stochastic opportunity set is discussed briefly in the text. This paper investigates an economy where stock prices follow a jump-diffusion process. The first part of the analysis derives a sufficient condition under which an instantaneous CAPM will characterize equilibrium expected returns. The sufficient condition is that the jump component of a stock's return must be unsystematic and diversifiable in the market portfolio. The second part of the paper is an empirical investigation of the satisfaction of this condition. The evidence is seen to be inconsistent with the satisfaction of this hypothesis, that is, the market portfolio appears to contain a jump component.

The paper develops a new class of financial market models. These models are based on generalised telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black–Scholes fundamental differential equation is derived, but, in contrast with the Black–Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging.

Predicting intraday stock jumps is a significant but challenging problem in finance. Due to the instantaneity and imperceptibility characteristics of intraday stock jumps, relevant studies on their predictability remain limited. This paper proposes a data‐driven approach to predict intraday stock jumps using the information embedded in liquidity measures and technical indicators. Specifically, a trading day is divided into a series of 5‐min intervals, and at the end of each interval, the candidate attributes defined by liquidity measures and technical indicators are input into machine learning algorithms to predict the arrival of a stock jump as well as its direction in the following 5‐min interval. An empirical study is conducted using level‐2 high‐frequency data of 1271 stocks on the Shenzhen Stock Exchange of China to validate our approach. The results provide initial evidence of the predictability of jump arrivals and jump directions using level‐2 stock data as well as the effectiveness of using a combination of liquidity measures and technical indicators for such prediction. We also reveal the superiority of using random forest compared with other machine learning algorithms in building prediction models. Importantly, our study provides a portable data‐driven approach that exploits liquidity and technical information from level‐2 stock data to predict intraday price jumps of individual stocks.

A Simple Robust Test for the Presence of Jumps in Asset Prices

An incomplete market with European type contingent claim based on two underlying assets whose price evolutions are assumed to be binary is considered. We obtain explicit formulas for upper and lower bounds for the rational price interval as well as for upper and lower hedging strategies. The obtained strategies are semi-self-financing in the sense that the extraction of funds is assumed at each time step with non-negative probability. The results are extended to the case where the stock price jumps are distributed over a closed rectangle and the pay-off function is convex. No assumptions are imposed on the joint distribution of the price jumps.

Stock prices often react sluggishly to news, producing gradual jumps and jump delays. Econometricians typically treat these sluggish reactions as microstructure effects and settle for a coarse sampling grid to guard against them. Synchronizing mistimed stock returns on a fine sampling grid allows us to better approximate the true common jumps in related stock prices.

Brfoo 1994, the one way measurcd pdormance of go public compa4y is earning afier tu, but on September 7, 1994 the Indonesian Institute olAccountants (IAI) published the statement of financial Accounting Standard (PSAK) No.2, "statement of Cash Flows" requires companiesto pubtish the statewent of cash flows beginning from January I, tggs. So investors had two kinds measurement of performance go public companies.The objective of study is to aplain the influence of informationcontent of accounting income, total cash Jlows, and components of cash flow with stock price in lidonesian manufacuring firms The accounting income is earning afiir ta,tc before extra ordinary item and discontinued operations and total cash flows is a sum of cash flow from operating activities, cash llow from investing activities, and cash tlow from financing activities.This study was constitute replicated study from Triyono and Yogiyanto (2000) about the association of information content of total cash flows, components of cash Jlows, and accoun:ting income with stock prices or stock returns. This study took sample frorn manufacnring firms lisfed in the Jakarta Stock Exciange @ni) from 1999-iOOZ tnoT"had pubtished aadited financial statement. Stock prices using monthly prices that hadended December 1999-2002. The statistics method used to test ltypotheses is a linier multiple regression. The model was considered: levek')odet. The empirical results with using the first model levels about the influ. hence information of accounting income and total cash flows with stock prices can be explained accounting income gave positive influence and significant with stock prices whereas total cash flows gcMe negative and tlgnil*nt with stock prices. In the second model levels about the influ- ,i"i ,nyn *ation of cash flow from operating actiu.ities, cash flow from investing activities, and cash flow from financing octivities with stock pri, i* b" explained, separated total gash fl9ws into.yomponents. of 'cash flows gave negative influence and significant with stock prices "rp"ifolly iash ltoi from aperating octivities and c-ash flow from finincing activities. In the third model levels obout influence information of acciunting income and components of cash Jlows with stock prices irn be expliined, accounting income gave positive inlluence and significont with stock prices whereas companents of cosh tlows gNe negative influence and significant with stock prices'Keywords : accounting Income, cash Flows, components of cashflows, levels model

This study examines the influence of macroeconomic news on price discontinuities in the S&P 500 index futures. Results document a strong association between macro news and price jumps. Over three‐fourths of the price jumps between 8:30 am and 8:35 am and over three‐fifths of the jumps between 10:00 am and 10:05 am are related to news released at 8:30 am and 10:30 am, respectively. Notably, among several types of news releases considered, Non‐farm Payroll and Consumer Confidence are found to be significantly related to price jumps. Our findings also provide insights into the speed of news absorption and the influence of alternative trading platforms on the jump return behavior. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:980–1001, 2014

The impact of successive jumps in price process on volatility is very important. We study the nature of self-motivation in price process using data from China’s stock market. Our empirical results suggest that: 1) Price jumps in China’s stock market are generally self-motivated, i.e., price jumps are clustering. 2) The jump intensity of China’s stock market is time-varying, and follows log-normal distribution, which indicates that the jump intensity is asymmetrical. 3) The jump intensities’ sequence exhibits typical long memory.

Jumps in Stock Prices: New Insights from Old Data

The Cross Section of Jumps around Earnings Announcements

We analyze the interaction between managerial decisions and firm value/asset prices by embedding the standard agency model of the firm into an otherwise standard asset pricing model.When the manager-agent's compensation depends on the firm's stock price performance, stock prices are set to induce the creation of future cash flows, instead of representing the discounted value of exogenous cash flows, as in the standard model.In our case, stock prices are formed via trading in the market to induce the managers to hold the number of shares consistent with the optimal effort level desired by the outside investors.We compare two price formation mechanisms, corresponding to two firm ownership structures.In the first, stock prices are formed competitively among a continuum of dispersed investors.In the second, stock prices are set by a single block shareholder, as a bargaining solution.Under both mechanisms there are persistent, dynamic, patterns of asst prices, The level of the equity premium and the return volatility depend on the risk aversion of the agents in the economy and the ownership structure of firms.

Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event‐risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy‐and‐hold strategies. Jumps in prices and volatility both have important effects.

Late Manifestations of the Rubella Syndrome in the Adult

Futures-Trading Activity and Jump Risk: Evidence From the Bitcoin Market