Affine Point Processes: Approximation and Efficient Simulation

Published Online:https://doi.org/10.1287/moor.2014.0696

References

  • Abate J, Whitt W (1992) The Fourier-series method for inverting transforms of probability distributions. QUESTA 10(1):5–88.Google Scholar
  • Aït-Sahalia Y, Cacho-Diaz J, Laeven RJA (2014) Modeling financial contagion using mutually exciting jump processes. J. Financial Econom. Forthcoming.Google Scholar
  • Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical Models Based on Counting Processes (Springer, New York).CrossrefGoogle Scholar
  • Azizpour S, Giesecke K, Kim B (2011) Premia for correlated default risk. J. Econom. Dynam. Control 35(8):1340–1357.CrossrefGoogle Scholar
  • Bacry E, Delattre S, Hoffmann M, Muzy JF (2013) Some limit theorems for Hawkes processes and application to financial statistics. Stochastic Processes Their Appl. 123:2475–2499.CrossrefGoogle Scholar
  • Bassamboo A, Jain S (2006) Efficient importance sampling for reduced form models in credit risk. Wieland FP, Perrone LF, Liu J, Lawson BG, Nicol DM, Fujimoto RM, eds. Proc. 2006 Winter Simulation Conf. (IEEE, Piscataway, NJ), 741–749.CrossrefGoogle Scholar
  • Berman A, Plemmons RJ (1987) Nonnegative Matrices in the Mathematical Sciences (SIAM, Philadelphia).Google Scholar
  • Blanchet J, Glynn PW, Meyn SP (2013) Large deviations for the empirical mean of an M/M/1 queue. QUESTA 73:425–446.Google Scholar
  • Bordenave C, Torrisi GL (2007) Large deviations of Poisson cluster processes. Stochastic Models 23:593–625.CrossrefGoogle Scholar
  • Bowsher CG (2007) Modelling security market events in continuous time: Intensity based, multivariate point process models. J. Econometrics 141:876–912.CrossrefGoogle Scholar
  • Brémaud P (1981) Point Processes and Queues: Martingale Dynamics (Springer, New York).CrossrefGoogle Scholar
  • Carmona R, Crépey S (2010) Particle methods for the estimation of Markovian credit portfolio loss distributions. Internat. J. Theoret. Appl. Finance 13(4):577–602.CrossrefGoogle Scholar
  • Cheridito P, Filipović D, Kimmel RL (2007) Market price of risk specification for affine models: Theory and evidence. J. Financial Econom. 83:123–170.CrossrefGoogle Scholar
  • Cheridito P, Filipović D, Yor M (2005) Equivalent and absolutely continuous measure changes for jump-diffusion processes. Ann. Appl. Probab. 15:1713–1732.CrossrefGoogle Scholar
  • Cvitanić J, Ma J, Zhang J (2012) Law of large numbers for self-exciting correlated defaults. Stochastic Processes Their Appl. 122(8):2781–2810.CrossrefGoogle Scholar
  • Dai Q, Singleton KJ (2000) Specification analysis of affine term structure models. J. Finance 55:1943–1978.CrossrefGoogle Scholar
  • Dai Pra P, Tolotti M (2009) Heterogeneous credit portfolios and the dynamics of the aggregate losses. Stochastic Processes Their Appl. 119:2913–2944.CrossrefGoogle Scholar
  • Dai Pra P, Runggaldier WJ, Sartori E, Tolotti M (2009) Large portfolio losses: A dynamic contagion model. Ann. Appl. Probab. 19:347–394.CrossrefGoogle Scholar
  • Daley DJ (1972) Asymptotic properties of stationary point processes with generalized clusters. Z. Wahrsch. Verw. Gebiete. 21:65–76.CrossrefGoogle Scholar
  • Del Moral P, Garnier J (2005) Genealogical particle analysis of rare events. Ann. Appl. Probab. 15:2496–2534.CrossrefGoogle Scholar
  • Dembo A, Zeitouni O (1998) Large Deviations Techniques and Applications, 2nd ed. (Springer, New York).CrossrefGoogle Scholar
  • Deng S, Giesecke K, Lai TL (2012) Sequential importance sampling and resampling for dynamic portfolio credit risk. Oper. Res. 60(1):78–91.LinkGoogle Scholar
  • Duffie D, Filipović D, Schachermayer W (2003) Affine processes and applications in finance. Ann. Appl. Probab. 13(3):984–1053.CrossrefGoogle Scholar
  • Duffie D, Pan J, Singleton KJ (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68(6):1343–1376.CrossrefGoogle Scholar
  • Duffy KR, Meyn SP (2010) Most likely paths to error when estimating the mean of a reflected random walk. Performance Evaluation 67(12):1290–1303.CrossrefGoogle Scholar
  • Embrechts P, Liniger T, Lin L (2011) Multivariate Hawkes processes: An application to financial data. J. Appl. Prob. 48:367–378.CrossrefGoogle Scholar
  • Errais E, Giesecke K, Goldberg LR (2010) Affine point processes and portfolio credit risk. SIAM J. Finan. Math. 1:642–665.CrossrefGoogle Scholar
  • Ethier SN, Kurtz TG (1986) Markov Processes: Characterization and Convergence (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Filipović D, Mayerhofer E, Schneider P (2013) Density approximations for multivariate affine jump-diffusion processes. J. Econometrics 176:93–111.CrossrefGoogle Scholar
  • Frommer A, Lang B, Schnurr M (2004) A comparison of the Moore and Miranda existence tests. Computing 72:349–354.CrossrefGoogle Scholar
  • Giesecke K, Shkolnik A (2014) Optimal importance sampling of default losses. Working paper.Google Scholar
  • Giesecke K, Weber S (2006) Credit contagion and aggregate losses. J. Econom. Dynam. Control 30:741–767.CrossrefGoogle Scholar
  • Giesecke K, Kim B, Zhu S (2011) Monte Carlo algorithms for default timing problems. Management Sci. 57(12):2115–2129.LinkGoogle Scholar
  • Giesecke K, Spiliopoulos K, Sowers RB (2013) Default clustering in large portfolios: Typical events. Ann. Appl. Probab. 23(1):348–385.CrossrefGoogle Scholar
  • Giesecke K, Kakavand H, Mousavi M, Takada H (2010) Exact and efficient simulation of correlated defaults. SIAM J. Finan. Math. 1:868–896.CrossrefGoogle Scholar
  • Giesecke K, Spiliopoulos K, Sowers RB, Sirignano JA (2015) Large portfolio asymptotics for loss from default. Math. Finance 25(1):77–114.CrossrefGoogle Scholar
  • Glasserman P (2003) Monte Carlo Methods in Financial Engineering (Springer, New York).CrossrefGoogle Scholar
  • Glasserman P, Kim K-K (2009) Saddlepoint approximation for affine jump-diffusion models. J. Econom. Dynam. Control 33:37–52.CrossrefGoogle Scholar
  • Horn RA, Johnson CR (1985) Matrix Analysis (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus, 2nd ed. (Springer, New York).Google Scholar
  • Kontoyiannis I, Meyn SP (2003) Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab. 13(1):304–362.CrossrefGoogle Scholar
  • Lépingle D, Mémin J (1978) Sur l’integrabilité uniforme des martingales exponentielles. Z. Wahrsch. Verw. Gebiete 42(3):175–203.CrossrefGoogle Scholar
  • Meyn SP, Tweedie RL (1993) Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Probab. 25:518–548.CrossrefGoogle Scholar
  • Miranda C (1940) Un’osservazione su un teorema di Brouwer. Bolletino Unione Mathematica Italiana 3:5–7.Google Scholar
  • Protter PE (2003) Stochastic Integration and Differential Equations, 2nd ed. (Springer, Berlin).Google Scholar
  • Spiliopoulos K, Sowers RB (2014) Default clustering in large pools: Large deviations. SIAM J. Finan. Math. Forthcoming.Google Scholar
  • Spiliopoulos K, Sirignano JA, Giesecke K (2014) Fluctuation analysis for the loss from default. Stoch. Proc. Appl. 124(7):2322–2362.CrossrefGoogle Scholar
  • Zhang X (2011) Computing rare-event probabilities for affine models and general state space Markov processes. Doctoral dissertation, Stanford University, Stanford, CA.Google Scholar
  • Zhang X, Glynn PW, Giesecke K, Blanchet J (2009) Rare event simulation for a generalized Hawkes process. Rossetti MD, Hill RR, Johansson B, Dunkin A, Ingalls RG, eds. Proc. 2009 Winter Simulation Conf. (IEEE, Piscataway, NJ),1291–1298.CrossrefGoogle Scholar
  • Zhu L (2013) Central limit theorem for nonlinear Hawkes processes. J. Appl. Probab. 50(3):760–771.CrossrefGoogle Scholar
  • Zhu L (2014) Process-level large deviations for nonlinear Hawkes point processes. Annales de l’Institut Henri Poincaré 50(3):845–871.CrossrefGoogle Scholar
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