Intensity Of Jumps Research Articles

Jump dynamics and volatility: Oil and the stock markets

Our study distinguishes itself from the prior studies within the oil and financial literature by not only examining the asymmetric effects of oil prices on stock returns, but also exploring the importance of structure changes in this dependency relationship. We retrieve daily data on S&P 500 and West Texas Intermediate (WTI) oil transactions covering the period from 1 January 1992 to 7 November 2006, and then transform the available data into daily returns. In contrast to the extant literature, in this study, consideration of expected, unexpected and negative unexpected oil price fluctuations is incorporated into the model of stock returns; we also focus on the ways in which oil price volatility, as opposed to general macroeconomic variables, can influence the stock market. We go on to implement the ARJI (Autoregressive Conditional Jump Intensity) model with structure changes, from which we conclude that high fluctuations in oil prices have asymmetric unexpected impacts on S&P 500 returns.

Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options

Standard empirical investigations of jump dynamics in returns and volatility are fairly complicated due to the presence of latent continuous-time factors. We present a new discrete-time framework that combines heteroskedastic processes with rich specifications of jumps in returns and volatility. Our models can be estimated with ease using standard maximum likelihood techniques. We provide a tractable risk neutralization framework for this class of models which allows for separate modeling of risk premia for the jump and normal innovations. We anchor our models in the literature by providing continuous time limits of the models. The models are evaluated by fitting a long sample of S&P500 index returns, and by valuing a large sample of options. We find strong empirical support for time-varying jump intensities. A model with jump intensity that is affine in the conditional variance performs particularly well both in return fitting and option valuation. Our implementation allows for multiple jumps per day, and the data indicate support for this model feature, most notably on Black Monday in October 1987. Our results also confirm the importance of jump risk premia for option valuation: jumps cannot significantly improve the performance of option pricing models unless sizeable jump risk premia are present.

Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options

Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options

Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate, Stochastic Volatility and Stochastic Jump Intensity World

We first derive closed form solutions for currency options, currency futures, future options and the term structures of interest rates in a diffusion-jump model of stochastic interest rate, stochastic volatility and time varying jump intensity in currency price. We demonstrate that the introduction of constant jump intensity in the nominal stochastic discount factor shifts the whole term structure of interest rates vertically but has no influence on its shape. However, when the jump intensity is endogenous (time varying) the shape of the term structure is influenced through the factor sensitivity of interest rates. We also document considerable improvement in currency option pricing precision over alternative models if the true model is diffusion-jump with endogenous intensity in a simulation experiment. We conclude that allowing for multidimensional interaction is of significant qualitative and quantitative importance for the pricing of currency options and for understanding the shape of the term structure.

Is twin behavior of Nikkei 225 index futures the same?

This study adopts the autoregressive conditional jump intensity (ARJI) model proposed by Chan and Maheu [J. Business Econ. Stat. 20 (2002) 377–389] to investigate the impact of news on SIMEX-Nikkei 225 and CME-Nikkei 225 (regards it as the twins). Empirical results demonstrate that the twins were captured by responses to various events; moreover, the twins have distinct jump intensity and risk. Finally, this investigation evaluates the lead–lag relationship between returns and jump behavior by the Granger causality test. Returns are based on unidirectional causality from two futures (the twins) to spot and feedback causality between the twins. Jump intensity reveal feedback causality between spot and the CME-Nikkei 225 and unidirectional causality from the CME-Nikkei 225 to in SIMEX-Nikkei 225.

Macroeconomic News, Announcements, and Stock Market Jump Intensity Dynamics

This paper examines the effect of macroeconomic releases on stock market volatility through a Poisson-Gaussian-GARCH process with time varying jump intensity, which is allowed to respond to such information. It is found that the day of the announcement, per se, has little impact on jump intensities. Employment releases are an exception. However, when macroeconomic surprises are considered, inflation shocks show persistent effects while monetary policy and employment shocks show only short-lived effects. Also, the jump intensity responds asymmetrically to macroeconomic shocks. Evidence that macroeconomic variables are relevant to explain jump dynamics and improve volatility forecasts on event days is provided.

Generic Quantum Markov Semigroups: the Fock Case

We introduce the class of generic quantum Markov semigroups. Within this class we study the class corresponding to the Fock case which is further split into four subclasses each of which contains both bounded and unbounded generators, depending on some global characteristics of the intensities of jumps. For the first two of these classes we find an explicit solution which reduces the problem of finding the quantum semigroup to the calculation of two classical semigroups, one of which is diagonal (in a suitable basis) and the other one is triangular (in the same basis). In the bounded case our formula gives the unique solution. In the unbounded case it gives one solution, which we conjecture to be the minimal one.

Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws

We are interested in the one-dimensional scalar conservation law ∂ t u(t,x)=νD αu(t,x)-∂ xA(u(t,x)) with fractional viscosity operator Dαv(x) = F-1(|ξ|αF(v)(ξ))(x) is the cumulative distribution function of a signed measure on R. We associate a nonlinear martingale problem with the Fokker-Planck equation obtained by spatial differentiation of the conservation law. After checking uniqueness for both the conservation law and the martingale problem, we prove existence thanks to a propagation-of-chaos result for systems of interacting particles with fixed intensity of jumps related to ν. The empirical cumulative distribution functions of the particles converge to the solution of the conservation law. As a consequence, it is possible to approximate this solution numerically by simulating the stochastic differential equation which gives the evolution of particles. Finally, when the intensity of jumps vanishes (ν→0) as the number of particles tends to +∞, we obtain that the empirical cumulative distribution functions converge to the unique entropy solution of the inviscid (ν=0) conservation law.

Bond Yields and the Federal Reserve

Bond yields respond to policy decisions by the Federal Reserve and vice versa. To learn about these responses, I model a high‐frequency policy rule based on yield curve information and an arbitrage‐free bond market. In continuous time, the Fed’s target is a pure jump process. Jump intensities depend on the state of the economy and the meeting calendar of the Federal Open Market Committee. The model has closed‐form solutions for yields as functions of a few state variables. Introducing monetary policy helps to match the whole yield curve, because the target is an observable state variable that pins down its short end and introduces important seasonalities around FOMC meetings. The volatility of yields is “snake shaped,” which the model explains with policy inertia. The policy rule crucially depends on the two‐year yield and describes Fed policy better than Taylor rules.

Density jumps in smoke flow along horizontal ceilings

The entrainment of ambient air by the formation of density jumps in horizontal smoke flows below a ceiling is analyzed with the help of the classical graphical method for analyzing hydraulic jumps. The analysis shows that although the formation and intensity of such jumps are determined by the nature of the upstream flow, which may be characterized by the upstream Froude number, the value of the entrainment in a density jump cannot be determined without specifying some of the downstream boundary conditions. However, we show that a maximum entrainment value exists for each upstream Froude number and an explicit equation for its value is derived. This equation, which may be used for design purposes, shows that entrainment due to density jumps can double and even triple the horizontal smoke mass flux.

Macroeconomic Foundations for Discontinuous Price Movements

This paper develops a dynamic general equilibrium asset pricing model to account for the discontinuous price movements commonly observed in the financial markets. We consider two possible sources: (1) jumps in the fundamental economy, as captured by the production technology, and (2) jumps in investors' perception of the economic risk, as captured by the intensity of jumps in the production process. The paper solves the dynamic portfolio decision problem and obtains in analytical forms the general equilibrium pricing of interest rates, bonds, and stocks. We also calibrate the model to the U.S. economy.

PROGRESSIVE JUMP AND LOWER BODY RESISTANCE TRAINING HIP BONE MASS IN PREMENOPAUSAL WOMEN

259 We studied the effects of one year of progressive high-impact (jump) and lower body resistance training on hip, spine and whole body bone mineral density (BMD) in 30-45 year old healthy, premenopausal women. Forty-five women participated in the training program and thirty-seven women (age = 39±5yrs; height = 166.4±6.5cm; weight = 66.7±10.6 kg) completed twelve months of exercise training (retention = 82%). Twenty-eight women were recruited as controls and twenty-six women (age = 41±3yrs; height = 165.1±9.7); weight = 66.8±13.4 kg) completed the year control period (retention = 93%). Controls were matched to the exercise group on hip BMD, age and weight. Baseline values of anthropometric and bone variables were not significantly different between exercisers and controls. Anthropometric variables did not change over the one year intervention. The training program was held three times per week and consisted of 100 jumps and 100 repetitions of a combination of resistance exercises: squats, front, side and back lunges, per session. Intensity of jumps and resistance exercise was increased via the use of weighted vests, and was expressed as a percentage of body weight (%BW). Jump and resistance intensity was progressively increased over the first ten months, and remained at 10%BW for jumps and 13%BW for resistance exercises for the final two months. Pre- and post-training measurements of the greater trochanter (GT) and femoral neck (FN) of the proximal femur, lumbar spine (LS), and whole body (WB) BMD (g/cm2) were measured via DXA Percent change, standard deviations, and significance values are shown in the table below:TableWe conclude that one year of jump and lower body resistance training significantly increases trochanteric bone mass in adult premenopausal women and, if maintained, could reduce fracture risk in later life. Supported by NASA GSRP and LifeFitness graduate student awards.

小川原湖に発生する傾斜プルームの音響探査観測

An inclined plume, generated by saline water, is visualized with an echo sounder. The output signal is stored as digital data so that the picture of reflection distribution can be reproduced with any intensity scale and size by post-processing. The pictures are compared with the data of salinity and temperature profiles obtained from STD measurement. The location of horizontal streaks in the picture of echo image corresponds to the depth of density jumps although the intensity of streaks does not correspond to the intensity of density jumps. The densimetric interface of the inclined plume can be identified as the lowest streak along the bottom.Richardson number of the plume(Ri) is estimated from the amplitude of stationary wave on the undulations of the bed topography based on an assumption of the local conservation of specific energy. The estimated Ri and the entrainment coefficient(E) calculated from the data of STD measurement show that E decreases rapidly when Ri approaches to 1.0. This fact means that the frequently used relationship of power law does not hold well.

Nonparametric inference for Markovian interval processes

Consider a p-variate counting process N = ( N ( i) ) with jump times { τ ( i) 1, τ ( i) 2, …}. Suppose that the intensity of jumps λ ( i) of N ( i) at time t depends on the time since its last jump as well as on the times since the last jumps of the other components, i.e. λ ( i) ( t) = α ( i) ( t − τ (1) N (1)( t −) , … t − τ ( p) N ( p) ( t −) ), where the α ( i) s are unknown, nonrandom functions. From observing one single trajectory of the process N over an increasing interval of time we estimate nonparametrically the functions α ( i) . The estimators are shown to be uniformly consistent over compact subsets. We derive a nonparametric asymptotic test for the hypothesis that α (1)( x 1, …, x p ) does not depend on x 2, …, x p , i.e. that N (1) is a renewal process. The results obtained are applied in the analysis of simultaneously recorded neuronal spike train series. In the example given, inhibition of one neuron (target) through another neuron (trigger) is characterized and identified as a geometric feature in the graphical representation of the estimate of α ( i) as a surface. Estimating the intensity of the target as a function of time of only the most recent trigger firing the estimate is displayed as a planar curve with a sharp minimum. This leads to a new method of assessing neural connectivity which is proposed as an alternative to existing cross-correlation-based methods.

Optimal stopping, free boundary, and American option in a jump-diffusion model

This paper considers the American put option valuation in a jump-diffusion model and relates this optimal-stopping problem to a parabolic integro-differential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its counterpart European price and the early exercise premium. Compared with the Black-Scholes (BS) [5] model, this premium has an additional term due to the presence of jumps. We prove the continuity of the free boundary and also give one estimate near maturity, generalizing a recent result of Barleset al. [3] for the BS model. Finally, we study the effect of the market price of jump risk and the intensity of jumps on the American put option price and its critical stock price.

Approximation of the Boltzmann equation by discrete velocity models

Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model.