2,907 research outputs found
A semi-Markov model for price returns
We study the high frequency price dynamics of traded stocks by a model of
returns using a semi-Markov approach. More precisely we assume that the
intraday return are described by a discrete time homogeneous semi-Markov
process and the overnight returns are modeled by a Markov chain. Based on this
assumptions we derived the equations for the first passage time distribution
and the volatility autocorreletion function. Theoretical results have been
compared with empirical findings from real data. In particular we analyzed high
frequency data from the Italian stock market from first of January 2007 until
end of December 2010. The semi-Markov hypothesis is also tested through a
nonparametric test of hypothesis
A semi-Markov model with memory for price changes
We study the high frequency price dynamics of traded stocks by a model of
returns using a semi-Markov approach. More precisely we assume that the
intraday returns are described by a discrete time homogeneous semi-Markov which
depends also on a memory index. The index is introduced to take into account
periods of high and low volatility in the market. First of all we derive the
equations governing the process and then theoretical results have been compared
with empirical findings from real data. In particular we analyzed high
frequency data from the Italian stock market from first of January 2007 until
end of December 2010
Semi Markov model for market microstructure
We introduce a new model for describing the fluctuations of a tick-by-tick
single asset price. Our model is based on Markov renewal processes. We consider
a point process associated to the timestamps of the price jumps, and marks
associated to price increments. By modeling the marks with a suitable Markov
chain, we can reproduce the strong mean-reversion of price returns known as
microstructure noise. Moreover, by using Markov renewal processes, we can model
the presence of spikes in intensity of market activity, i.e. the volatility
clustering, and consider dependence between price increments and jump times. We
also provide simple parametric and nonparametric statistical procedures for the
estimation of our model. We obtain closed-form formula for the mean signature
plot, and show the diffusive behavior of our model at large scale limit. We
illustrate our results by numerical simulations, and that our model is
consistent with empirical data on the Euribor future.Comment: number of pages: 2
Brownian excursions outside a corridor and two-sided Parisian options
In this paper, we study the excursion time of a Brownian motion with drift outside a corridor by using a four states semi-Markov model. In mathematical finance, these results have an important application in the valuation of double barrier Parisian options. In this paper, we obtain an explicit expression for the Laplace transform of its price
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code
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