Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userErgodicity and scaling limit of a constrained multivariate Hawkes process
488
0
0.0
(
0
)
Authors
Ban Zheng
Ask ChatGPT about the research
No Arabic abstract
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional constraint variable, whose evolution is driven by the point process. We study this process in the special case where the fertility function is exponential so that the process is entirely described by an underlying Markov chain, which includes the constraint variable. Some conditions on the parameters are established to ensure the ergodicity of the chain. Moreover, scaling limits are derived for the integrated point process. This study is primarily motivated by the stochastic modelling of a limit order book for high frequency financial data analysis.
rate research
Read More
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection of intensity bursts within the Hawkes process framework. By using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown. Moreover, the initial time of the burst can be determined with a precision given by the typical inter-event time. We apply our methodology to the mid-price change in FX markets showing that these bursts are frequent and that only a relatively small fraction is associated to news arrival. We show lead-lag relations in intensity burst occurrence across different FX rates and we discuss their relation with price jumps.
In this paper, we provide upper bounds on the d2 distance between a large class of functionals of a multivariate compound Hawkes process and a given Gaussian vector. This is proven using Malliavins calculus defined on an underlying Poisson embedding. The upper bound is then used to infer the speed of convergence of Central Limit Theorems for the multivariate compound Hawkes process with exponential kernels as the observation time T goes to infinity.
Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. In this paper we propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes option pricing model. This new measure accounts for the price of the strangle, relative to the Present Value of the spread between the two strikes, all expressed, after a natural re-parameterization, in terms of delta and a volatility parameter. We show that under the standard BS option pricing model, this measure of relative value is bounded by a simple function of delta only and is independent of the time to expiry, the price of the underlying security or the prevailing volatility used in the pricing model. We demonstrate how this bound can be used as a quick {it benchmark} to assess, regardless the market volatility, the duration of the contract or the price of the underlying security, the market (relative) value of the $delta-$strangle in comparison to its BS (relative) price. In fact, the explicit and simple expression for this measure and bound allows us to also study in detail the strangles exit strategy and the corresponding {it optimal} choice for a value of delta.
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c`adl`ag functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to Levy driven SDEs under some Lyapunov-type stability assumptions. As a numerical application of this work, we show that this procedure gives an efficient way of option pricing in stochastic volatility models.
The art of systematic financial trading evolved with an array of approaches, ranging from simple strategies to complex algorithms all relying, primary, on aspects of time-series analysis. Recently, after visiting the trading floor of a leading financial institution, we noticed that traders always execute their trade orders while observing images of financial time-series on their screens. In this work, we built upon the success in image recognition and examine the value in transforming the traditional time-series analysis to that of image classification. We create a large sample of financial time-series images encoded as candlestick (Box and Whisker) charts and label the samples following three algebraically-defined binary trade strategies. Using the images, we train over a dozen machine-learning classification models and find that the algorithms are very efficient in recovering the complicated, multiscale label-generating rules when the data is represented visually. We suggest that the transformation of continuous numeric time-series classification problem to a vision problem is useful for recovering signals typical of technical analysis.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
