291
Views
5
CrossRef citations to date
0
Altmetric
Research Papers

A self-exciting switching jump diffusion: properties, calibration and hitting time

&
Pages 407-426 | Received 25 Oct 2017, Accepted 13 Jul 2018, Published online: 03 Sep 2018

References

  • Abate, J. and Whitt, W., A unified framework for numerically inverting Laplace transforms. INFORMS J. Comput., 2006, 18(4), 408–421. doi: 10.1287/ijoc.1050.0137
  • Aït-Sahalia, Y., Cacho-Diaz, J. and Laeven, R.J.A., Modeling financial contagion using mutually exciting jump processes. J. Financ. Econ., 2015, 117, 585–606. doi: 10.1016/j.jfineco.2015.03.002
  • Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J.F., Modelling microstructure noise with mutually exciting point processes. Quant. Finance, 2013, 13, 65–77. doi: 10.1080/14697688.2011.647054
  • Bacry, E., Mastromatteo, I. and Muzy, J.F., Hawkes processes in finance. Mark. Microstruct. Liq., 2015, 1(1), 1–59.
  • Boswijk, P., Laeven, R.J.A and Lalu, A., Asset returns with self-exciting jumps: Option pricing and estimation with a continuum of moments. Working paper, 2015.
  • Boyarchenko, S. and Levendorskii, S., American options in regime-switching models. SIAM J. Control Optim., 2009, 48(3), 1353–1376. doi: 10.1137/070682897
  • Buffington, J. and Elliott, R.J., American options with regime switching. Int. J. Theoretical Appl. Financ., 2002, 5, 497–514. doi: 10.1142/S0219024902001523
  • Carr, P. and Madan, D., Option valuation using the fast fourier transform. J. Comput. Financ., 1999, 2, 61–73. doi: 10.21314/JCF.1999.043
  • Carr, P. and Wu, L., Leverage effect, volatility feedback, and self-exciting market disruptions. J. Financ. Quant. Anal., 2016, 52, 2119–2156. doi: 10.1017/S0022109017000564
  • Chavez-Demoulin, V. and McGill, J., High-frequency financial data modeling using Hawkes processes. J. Bank. Financ., 2012, 36(6), 3415–3426. doi: 10.1016/j.jbankfin.2012.08.011
  • Chen, K. and Poon, S.-H., Variance swap premium under stochastic volatility and self-exciting jumps. Working paper. SSRN-id2200172, 2013.
  • Chourdakis, K., Switching Lévy models in continuous time: Finite distributions and option pricing. Working paper. SSRN: 838924, 2005.
  • Dassios, A. and Jang, J., Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity. Financ. Stoch., 2003, 7, 73–95. doi: 10.1007/s007800200079
  • Dassios, A. and Zhao, H., A dynamic contagion process. Adv. Appl. Probab., 2011, 43, 814–846. doi: 10.1239/aap/1316792671
  • Dassios, A. and Zhao, H., A Markov chain model for contagion. Risks, 2014, 2(4), 434–455. doi: 10.3390/risks2040434
  • Embrechts, P., Liniger, T. and Lu, L., Multivariate Hawkes processes: An application to financial data. J. Appl. Probab., 2011, 48(A), 367–378. doi: 10.1239/jap/1318940477
  • Errais, E., Giesecke, K. and Goldberg, L., Affine point processes and portfolio credit risk. SIAM J. Financ. Math., 2010, 1, 642–665. doi: 10.1137/090771272
  • Ficura, M., Modelling jump clustering in the four major foreign exchange rates using high-frequency returns and cross-exciting jump processes. Procedia Econ. Financ., 2015, 25, 208–219. doi: 10.1016/S2212-5671(15)00731-5
  • Fulop, A., Li, J. and Yu, J., Self-exciting jumps, learning, and asset pricing implications. Rev. Financ. Studies, 2015, 28, 876–912. doi: 10.1093/rfs/hhu078.
  • Guidolin, M. and Timmermann, A., International asset allocation under regime switching, skew, and kurtosis preferences. Rev. Financ. Studies, 2008, 21(2), 889–935. doi: 10.1093/rfs/hhn006
  • Hainaut, D., A model for interest rates with clustering effects. Quant. Finance, 2016a, 16(8), 1203–1218. doi: 10.1080/14697688.2015.1135251
  • Hainaut, D., Impact of volatility clustering on equity indexed annuities. Insur. Math. Econ., 2016b, 71, 367–381. doi: 10.1016/j.insmatheco.2016.10.009
  • Hainaut, D. and Colwell, D., A structural model for credit risk with switching processes and synchronous jumps. Eur. J. Financ., 2016, 22(11), 1040–1062. doi: 10.1080/1351847X.2014.924079
  • Hainaut, D. and Moraux, F., Hedging of options in presence of jump clustering. J. Comput. Financ., 2018, forthcoming.
  • Hamilton, J.D., A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 1989, 57(2), 357–384. doi: 10.2307/1912559
  • Hawkes, A., Spectra of some mutually exciting point processes. J. R. Stat. Soc. Ser. B, 1971, 33, 438–443. doi:10.1093/biomet/58.1.83.
  • 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. doi: 10.1093/rfs/6.2.327
  • Honda, T., Optimal portfolio choice for unobservable and regime-switching mean returns. J. Econ. Dyn. Control, 2003, 28(1), 45–78. doi: 10.1016/S0165-1889(02)00106-9
  • Jiang, Z. and Pistorius, M.R., On perpetual American put valuation and first-passage in a regime-switching model with jumps. Financ. Stoch., 2008, 12(2), 331–355. doi: 10.1007/s00780-008-0065-9
  • Kou, S.G., A jump-diffusion model for option pricing. Manage. Sci., 2002, 48(8), 1086–1101. doi: 10.1287/mnsc.48.8.1086.166
  • Kou, S.G. and Wang, H., First passage times of a jump diffusion process. Adv. Appl. Probab., 2003, 35(2), 504–531. doi: 10.1239/aap/1051201658
  • Le Courtois, O. and Su, X., Structural pricing of CoCos and deposit insurance with regime switching and jumps. Working paper. AFFI International Conference, 2017.
  • Levendorski, S., American and European options in multi-factor jump-diffusion models, near expiry. Financ. Stoch., 2008, 12(4), 541–560. doi: 10.1007/s00780-008-0070-z
  • Rangel, J., Macroeconomic news, announcements, and stock market jump intensity dynamics. J. Bank. Financ., 2011, 35(5), 1263–1276. doi: 10.1016/j.jbankfin.2010.10.009.
  • Rogers, L.C.G., Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Ann. Appl. Probab., 1994, 4(2), 390–413. doi: 10.1214/aoap/1177005065
  • Yong, M.K. and Xu, S.W., Pricing vulnerable options with jump clustering. J Fut Mark, 2017, 37(12), 1155–1178. doi: 10.1002/fut.21843

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.