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JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes
[article]
2015
arXiv
pre-print
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We derive the small-variance asymptotics for parametric and nonparametric MJPs for both directly observed and hidden state models. ...
We take a small-variance asymptotics (SVA) approach to overcome these limitations. ...
ACKNOWLEDGMENTS Thanks to Monir Hajiaghayi, Matthew Johnson, and Tejas Kulkarni for helpful comments and discussions. JHH was supported by the U.S. ...
arXiv:1503.00332v3
fatcat:hngrdfssmzclvfamgiy5v3vuwy
Asset Pricing with Matrix Jump Diffusions
2008
Social Science Research Network
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This paper introduces a new class of matrix-valued affine jump diffusions that are convenient for modeling multivariate risk factors in many financial and econometric problems. ...
We provide an analytical transform analysis for this class of models, leading to an analytical treatment of a broad class of multivariate valuation and econometric problems. ...
They find a jump mean of 0.03%, a jump mean intensity of 0.08, and a jump volatility of 0.41%. ...
doi:10.2139/ssrn.1274482
fatcat:2xmyddfksnfzvatwbf6e4tzbay
Stochastic-Volatility, Jump-Diffusion Optimal Portfolio Problem with Jumps in Returns and Volatility
2011
Social Science Research Network
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variable, instead of the ordinary integro-differential equation (OIDE) found for the pure jump-diffusion model of the wealth process. ...
Main modifications for the usual constant relative risk aversion (CRRA) power utility model are for handling the partial integro-differential equation (PIDE) resulting from the additional variance independent ...
The stochastic processes G s (t) and P s (t) are assumed to be Markov and pairwise independent. ...
doi:10.2139/ssrn.1874872
fatcat:4oh3ujsjsngbtlhyo337zsjvay
The surprise element: jumps in interest rates
2002
Journal of Econometrics
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Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior. ...
Estimators are used based on analytical derivations of the characteristic functions and moments of jump-diffusion stochastic processes for a range of jump distributions, and are extended to discrete-time ...
From Section 2.3, the conditional variance of the jump-diffusion process is: µ 2 − µ 2 1 = v 2 + hE J 2 2k (1 − e −2kT ). ...
doi:10.1016/s0304-4076(01)00085-9
fatcat:xhdwajta6zb4nl5wjymcsp7w5q
Jumps in Equity Index Returns Before and During the Recent Financial Crisis: A Bayesian Analysis
2017
Management science
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1980 to 2013 well; the model outperforms existing ones (e.g., models with variance-gamma jumps or jumps in volatility) during the crisis and is at least comparable before the crisis. ...
For the first question, on the basis of the model and the data sets, we observe that during the crisis, negative jump rate increased significantly, although there was little change in the average negative ...
Acknowledgments The authors thank two anonymous referees and the associate editor for helpful comments. ...
doi:10.1287/mnsc.2015.2359
fatcat:vw2yymu7kjfejhc4fmomz4u3du
Survey of maneuvering targettracking . part I: dynamic models
2003
IEEE Transactions on Aerospace and Electronic Systems
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It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target ...
This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. ...
ACKNOWLEDGMENTS The authors would like to thank the following people for their comments on the conference version [13] and/or draft of this paper: Yaakov Bar-Shalom, Edward Beadle, Jeff Bell, Bob Bishop ...
doi:10.1109/taes.2003.1261132
fatcat:baur7qlwavg2fjqefk5x4dc4lq
Petroleum Concessions with Extendible Options: Investment Timing and Value Using Mean Reversion and Jump Processes for Oil Prices
1999
Social Science Research Network
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The stochastic model of jump+mean-reversion for the oil prices has more economic logic than previous models used in real options literature, considering that normal news causes continuous small mean-reverting ...
Although they don't suggest explicitly the jump+mean-reversion together, they indicate separately both processes as possible good models for oil prices and the importance for oil firms to take these features ...
The interface have three stochastic processes available to choose to perform the calculus for the extendible option problem: a) mean-reversion+jump, with the random jump using two truncated-normal distribution ...
doi:10.2139/ssrn.159692
fatcat:i5na6vvxy5dnhcezal3xzlqzsi
Central limit theorem for the size of the range of a renewal process
2005
Statistics and Probability Letters
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We study the range of a Markov chain moving forward on the positive integers. For every position, there is a probability distribution on the size of the next forward jump. ...
Taking a scaling limit as the means and variances of these distributions approach given continuous functions of position, there is a Gaussian limit law for the number of sites hit in a given rescaled interval ...
He would like to thank the Department of Mathematics and Statistics for the invitation, and Christel and Stefan Geiss for their hospitality. ...
doi:10.1016/j.spl.2004.12.011
fatcat:42tcrtehwbeopfo7xspfv7ixni
International Correlation Asymmetries: Frequent-But-Small and Infrequent-But-Large Equity Returns
2014
Social Science Research Network
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We decompose returns into frequent-but-small diffusion and infrequent-but-large jumps, and derive an estimation method for many countries. ...
We find that correlations due to jumps, not diffusion, increase markedly in bad markets leading to correlation breaks during crises. ...
Let's first look at the portfolio weights of the models with one regime, without jumps (mean-variance) and with jumps. ...
doi:10.2139/ssrn.2529613
fatcat:bsa7yndi5vflniyvwoohm3jmwa
An Empirical Examination of Deregulated Electricity Prices
2001
Social Science Research Network
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We begin by examining the distributional and temporal properties of the price process in a non-parametric framework. This analysis is followed by estimating several financial and statistical models. ...
Clear from the parameter estimates in Tables 2 and 5 is that electricity prices are not reasonably approximated by a univariate Markov process. ...
Model 3a: Jump-Diffusion Process As a first attempt to capture the leptokurtosis present in the price series, we turn to a popular extension of the standard diffusion process: the jump-diffusion process ...
doi:10.2139/ssrn.294382
fatcat:m6hx767iijevpnlp7dy5wwsknm
A Stochastic Processes Toolkit for Risk Management
2007
Social Science Research Network
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Once the process has been calibrated, typically through maximum likelihood estimation, one may simulate the risk factor and build future scenarios for the risky portfolio. ...
This paper does not aim at being exhaustive, but gives examples and a feeling for practically implementable models allowing for stylised features in the data. ...
Suppose then that the Jump size Y is normally distributed, with mean µ Y and variance σ 2 Y . For small ∆t, one knows that there will be possibly just one jump. ...
doi:10.2139/ssrn.1109160
fatcat:b7fguiiqmvg3rnexkcb63qfgaa
A Stochastic Processes Toolkit for Risk Management
[article]
2008
arXiv
pre-print
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Once the process has been calibrated, typically through maximum likelihood estimation, one may simulate the risk factor and build future scenarios for the risky portfolio. ...
This paper does not aim at being exhaustive, but gives examples and a feeling for practically implementable models allowing for stylised features in the data. ...
Suppose then that the Jump size Y is normally distributed, with mean µ Y and variance σ 2 Y . For small ∆t, one knows that there will be possibly just one jump. ...
arXiv:0812.4210v1
fatcat:umwdvjbenfg7vethw5q3ft5btu
Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps
[chapter]
2013
Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities
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We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. We also present a lower bound for delay as a measure of risk. ...
We study the valuation of the variance swaps under stochastic volatility with delay and jumps. ...
The authors would like to thank an anonymous referee very much for valuable comments and suggections that improved the present paper. The authors remain responsible for any errors in this paper. ...
doi:10.1142/9789814440134_0009
fatcat:dhdokgirunetdhnyom4ky25bzu
Random decompositions of Eulerian statistics
[article]
2021
arXiv
pre-print
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We define a random process to decompose the statistics over compositions of integers. ...
It is shown that the numbers of descents in random involutions and in random derangements are asymptotically normal with a rate of convergence of order n^-1/2 and n^-1/3 respectively. ...
One-jump means that the particles move one step forward together, while two-jump means that the particle in the back moves two step forward and the particle in the front stays at its position. ...
arXiv:2103.07498v1
fatcat:guxc4rtuyfbrzioesydwzvcbqu
Approximate hedging with proportional transaction costs in stochastic volatility models with jumps
[article]
2019
arXiv
pre-print
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Assuming some mild condition on the jump size distribution we show that transaction costs can be approximately compensated by applying the Leland adjusting volatility principle and the asymptotic property ...
The study also confirms that for the case of constant trading cost rate, the approximate results established by Kabanov and Safarian (1997)and by Pergamenschikov (2003) are still valid in jump-diffusion ...
To see this issue, let us assume that y is a Markov process. ...
arXiv:1505.02627v2
fatcat:ywyhzcnnxjggdhpngmv2biioba
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