Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnalytic Moments for GARCH Processes
49
0
0.0
(
0
)
Added by
Carol Alexander Prof.
Publication date
2018
fields
Financial
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. Our empirical study yields excellent approximate predictive distributions from these analytic moments, thus precluding the need for time-consuming simulations.
rate research
Read More
Several academics have studied the ability of hybrid models mixing univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and neural networks to deliver better volatility predictions than purely econometric models. Despite presenting very promising results, the generalization of such models to the multivariate case has yet to be studied. Moreover, very few papers have examined the ability of neural networks to predict the covariance matrix of asset returns, and all use a rather small number of assets, thus not addressing what is known as the curse of dimensionality. The goal of this paper is to investigate the ability of hybrid models, mixing GARCH processes and neural networks, to forecast covariance matrices of asset returns. To do so, we propose a new model, based on multivariate GARCHs that decompose volatility and correlation predictions. The volatilities are here forecast using hybrid neural networks while correlations follow a traditional econometric process. After implementing the models in a minimum variance portfolio framework, our results are as follows. First, the addition of GARCH parameters as inputs is beneficial to the model proposed. Second, the use of one-hot-encoding to help the neural network differentiate between each stock improves the performance. Third, the new model proposed is very promising as it not only outperforms the equally weighted portfolio, but also by a significant margin its econometric counterpart that uses univariate GARCHs to predict the volatilities.
We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov type strategies we find that martingale null hypotheses are rejected for many stock price processes.
This paper proposes a hybrid credit risk model, in closed form, to price vulnerable options with stochastic volatility. The distinctive features of the model are threefold. First, both the underlying and the option issuers assets follow the Heston-Nandi GARCH model with their conditional variance being readily estimated and implemented solely on the basis of the observable prices in the market. Second, the model incorporates both idiosyncratic and systematic risks into the asset dynamics of the underlying and the option issuer, as well as the intensity process. Finally, the explicit pricing formula of vulnerable options enables us to undertake the comparative statistics analysis.
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.
The Epps effect is key phenomenology relating to high frequency correlation dynamics in the financial markets. We argue that it can be used to determine whether trades at a tick-by-tick scale are best represented as samples from a Brownian diffusion, perhaps dressed with jumps; or as samples from truly discrete events represented as connected point processes. This can answer the question of whether correlations are better understood as an emergent time scale dependent property. In other words: Is the Epps effect a bias? To this end, we derive the Epps effect arising from asynchrony and provide a refined method to correct for the effect. The correction is compared against two existing methods correcting for asynchrony. We propose three experiments to discriminate between possible underlying representations: whether the data is best thought to be generated by discrete connected events (as proxied by a D-type Hawkes process), or if they can be approximated to arise from Brownian diffusions, with or without jumps. We then demonstrate how the Hawkes representation easily recovers the phenomenology reported in the literature; phenomenology that cannot be recovered using a Brownian representation, without additional ad-hoc model complexity, even with jumps. The experiments are applied to trade and quote data from the Johannesburg Stock Exchange. We find evidence suggesting that high frequency correlation dynamics are most faithfully recovered when tick-by-tick data is represented as a web of inter-connected discrete events rather than sampled or averaged from underlying continuous Brownian diffusions irrespective of whether or not they are dressed with jumps.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
