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Research Papers

Quadratic Hawkes processes for financial prices

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Pages 171-188 | Received 05 Oct 2015, Accepted 12 May 2016, Published online: 15 Jul 2016

References

  • Allez, R. and Bouchaud, J.-P., Individual and collective stock dynamics: Intra-day seasonalities. New J. Phys., 2011, 13(2), 025010.
  • Arneodo, A., Muzy, J.-F. and Sornette, D., Direct causal cascade in the stock market. Eur. Phys. J. B-Condens Matter Complex Syst., 1998, 2(2), 277–282.
  • Bacry, E. and Muzy, J.-F., Hawkes model for price and trades high-frequency dynamics. Quant. Finance, 2014, 14(7), 1147–1166.
  • Bacry, E., Delour, J. and Muzy, J.-F., Modelling financial time series using multifractal random walks. Physica A, 2001, 299(1), 84–92.
  • Bacry, E., Kozhemyak, A. and Muzy, J.-F., Continuous cascade models for asset returns. J. Econ. Dyn. Control, 2008, 32(1), 156–199.
  • Bacry, E., Gloter, A., Hoffmann, M. and Muzy, J.F., Multifractal analysis in a mixed asymptotic framework. Ann. Appl. Probab., 2010, 20(5), 1729–1760.
  • Bacry, E., Dayri, K. and Muzy, J.-F., Non-parametric kernel estimation for symmetric hawkes processes. Application to high frequency financial data. Eur. Phys. J. B, 2012a, 85(5), 1–12.
  • Bacry, E., Duvernet, L. and Muzy, J.-F., Continuous-time skewed multifractal processes as a model for financial returns. J. Appl. Probab., 2012b, 49(2), 482–502.
  • Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J.-F., Modelling microstructure noise with mutually exciting point processes. Quant. Finance, 2013, 13(1), 65–77.
  • Bacry, E., Mastromatteo, I. and Muzy, J.-F., Hawkes processes in finance. 2015. preprint arXiv:1502.04592.
  • Bergomi, L., Smile dynamics ii, iii and iv. Risk Mag., 2009.
  • Blanc, P., Modélisation de la volatilité des marchés financiers par une structure arch multifréquence. Master’s thesis [Modeling the volatility of financial markets with a multifrequency ARCH structure], Université de Paris VI Pierre et Marie Curie, 2012. Available upon request.
  • Blanc, P., Chicheportiche, R. and Bouchaud, J.-P., The fine structure of volatility feedback ii: Overnight and intra-day effects. Physica A, 2014, 402, 58–75.
  • Brémaud, P. and Massoulié, L., Hawkes branching point processes without ancestors. J. Appl. Probab., 2001, 38(1), 122–135.
  • Buescu, J., Positive integral operators in unbounded domains. J. Math. Anal. Appl., 2004, 296(1), 244–255.
  • Challet, D., Marsili, M. and Zhang, Y.-C., Minority games: Interacting agents in financial markets. OUP Catalogue, 2013.
  • Chicheportiche, R. and Bouchaud, J.-P., The fine-structure of volatility feedback i: Multi-scale self-reflexivity. Physica A, 2014, 410, 174–195.
  • Cox, J.C., Ingersoll, J.E. Jr and Ross, S.A., An intertemporal general equilibrium model of asset prices. Econometrica, 1985, 363–384.
  • Cristelli, M., Pietronero, L. and Zaccaria, A., Critical overview of agent-based models for economics. In Proceedings of the International School of Physics “Enrico Fermi” Course, Complex Materials in Physics and Biology, edited by F. Mallamace and H.E. Stanley, Vol. CLXXVI, 2011 (Italian Physical Society: Bologna).
  • Filimonov, V. and Sornette, D., Apparent criticality and calibration issues in the hawkes self-excited point process model: Application to high-frequency financial data. Quant. Finance, 2015, 1–22 (ahead-of-print).
  • Forman, J.L. and Sørensen, M., The pearson diffusions: A class of statistically tractable diffusion processes. Scand. J. Statistics, 2008, 35(3), 438–465.
  • Gatheral, J., Jaisson, T. and Rosenbaum, M., Volatility is rough. 2014. Available at SSRN 2509457.
  • Gopikrishnan, P., Plerou, V., Amaral, L.A.N., Meyer, M. and Stanley, H.E., Scaling of the distribution of fluctuations of financial market indices. Phys. Rev. E, 1999, 60(5), 5305.
  • Hardiman, S.J. and Bouchaud, J.-P., Branching-ratio approximation for the self-exciting hawkes process. Phys. Rev. E, 2014, 90(6), 062807.
  • Hardiman, S.J., Bercot, N. and Bouchaud, J.-P., Critical reflexivity in financial markets: A hawkes process analysis. Eur. Phys. J. B, 2013, 86(10), 1–9.
  • Hawkes, A.G., Spectra of some self-exciting and mutually exciting point processes. Biometrika, 1971, 58(1), 83–90.
  • Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 1993, 6(2), 327–343.
  • Hill, B.M., A simple general approach to inference about the tail of a distribution. Ann. Stat., 1975, 3(5), 1163–1174.
  • Jaisson, T. and Rosenbaum, M., Limit theorems for nearly unstable hawkes processes. 2013. preprint arXiv:1310.2033
  • Jaisson, T. and Rosenbaum, M., Rough fractional diffusions as scaling limit of nearly unstable heavy tailed hawkes processes. 2015, forthcoming.
  • Kallenberg, O., Foundations of Modern Probability, 2002 (Springer Science & Business Media: Berlin).
  • Lallouache, M. and Challet, D., Statistically significant fits of hawkes processes to financial data. 2014. Available at SSRN 2450101.
  • Laub, P.J., Taimre, T. and Pollett, P.K., Hawkes processes. 2015. preprint arXiv:1507.02822.
  • Matteo, T.D., Aste, T. and Dacorogna, M.M., Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development. J. Bank. Finance, 2005, 29(4), 827–851.
  • Müller, U.A., Dacorogna, M.M., Davé, R.D., Olsen, R.B., Pictet, O.V. and von Weizsäcker, J.E., Volatilities of different time resolutions -- Analyzing the dynamics of market components. J. Emp. Finance, 1997, 4(2), 213–239.
  • Plerou, V., Gopikrishnan, P., Amaral, L.A.N., Meyer, M. and Stanley, H.E., Scaling of the distribution of price fluctuations of individual companies. Phys. Rev. E, 1999, 60(6), 6519.
  • Pomeau, Y., Symétrie des fluctuations dans le renversement du temps. J. Phys., 1982, 43(6), 859–867.
  • Ramsey, J.B. and Rothman, P., Time irreversibility and business cycle asymmetry. J. Money Credit Bank., 1996, 1–21.
  • Ramsey, J.B. and Rothman, P., Characterization of the time irreversibility of economic time series: Estimators and test statistics, In CV Starr Center for Applied Economics, 1988 (New York University, Faculty of Arts and Science, Department of Economics, New York).
  • Saichev, A. and Sornette, D., Generation-by-generation dissection of the response function in long memory epidemic processes. Eur. Phys. J. B, 2010, 75(3), 343–355.
  • Sentana, E., Quadratic arch models. Rev. Econ. Stud., 1995, 62(4), 639–661.
  • Stein, E.M. and Stein, J.C., Stock price distributions with stochastic volatility: An analytic approach. Rev. Financial Stud., 1991, 4(4), 727–752.
  • Zumbach, G., Time reversal invariance in finance. Quant. Finance, 2009, 9(5), 505–515.
  • Zumbach, G., Volatility conditional on price trends. Quant. Finance, 2010, 10(4), 431–442.
  • Zumbach, G., Cross-sectional universalities in financial time series. Quant. Finance, 2015, 15(12), 1901–1912.
  • Zumbach, G. and Lynch, P., Heterogeneous volatility cascade in financial markets. Physica A, 2001, 298(3–4), 521–529.

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