Unbiased Sensitivity Estimation of One-Dimensional Diffusion Processes

Published Online:https://doi.org/10.1287/moor.2017.0926

References

  • Aït-Sahalia Y (2002) Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach. Econometrica 70(1):223–262.CrossrefGoogle Scholar
  • Asmussen S, Glynn PW (2007) Stochastic Simulation: Algorithms and Analysis, Vol. 57 (Springer Science & Business Media, New York).CrossrefGoogle Scholar
  • Beskos A, Papaspiliopoulos O, Roberts GO (2006) Retrospective exact simulation of diffusion sample paths with applications. Bernoulli 12(6):1077–1098.CrossrefGoogle Scholar
  • Beskos A, Papaspiliopoulos O, Roberts GO (2008) A factorisation of diffusion measure and finite sample path constructions. Methodology Comput. Appl. Probab. 10(1):85–104.CrossrefGoogle Scholar
  • Beskos A, Papaspiliopoulos O, Roberts GO, Fearnhead P (2006) Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion). J. Roy. Statist. Soc.: Ser. B (Statist. Methodology) 68(3):333–382.CrossrefGoogle Scholar
  • Beskos A, Roberts GO, (2005) Exact simulation of diffusions. Ann. Appl. Probab. 15(4):2422–2444.CrossrefGoogle Scholar
  • Broadie M, Glasserman P (1996) Estimating security price derivatives using simulation. Management Sci. 42(2):269–285.LinkGoogle Scholar
  • Casella B, Roberts GO (2011) Exact simulation of jump-diffusion processes with Monte Carlo applications. Methodology Comput. Appl. Probab. 13(3):449–473.CrossrefGoogle Scholar
  • Chen N, Huang Z (2012) Brownian meanders, importance sampling and unbiased simulation of diffusion extremes. Oper. Res. Lett. 40(6):554–563.CrossrefGoogle Scholar
  • Chen N, Huang Z (2013) Localization and exact simulation of Brownian motion-driven stochastic differential equations. Math. Oper. Res. 38(3):591–616.LinkGoogle Scholar
  • Di Nunno G, Øksendal BK, Proske F (2009) Malliavin Calculus for Lévy Processes with Applications to Finance, Vol. 2 (Springer, Berlin).CrossrefGoogle Scholar
  • Fournié E, Lasry JM, Lebuchoux J, Lions PL (2001) Applications of Malliavin calculus to Monte-Carlo methods in finance. II. Finance Stochastics 5(2):201–236.CrossrefGoogle Scholar
  • Fournié E, Lasry JM, Lebuchoux J, Lions PL, Touzi N (1999) Applications of Malliavin calculus to Monte Carlo methods in finance. Finance Stochastics 3(4):391–412.CrossrefGoogle Scholar
  • Giesecke K, Smelov D (2013) Exact sampling of jump diffusions. Oper. Res. 61(4):894–907.LinkGoogle Scholar
  • Glasserman P (2013) Monte Carlo Methods in Financial Engineering, Vol. 53 (Springer Science & Business Media, New York).Google Scholar
  • Jourdain B, Sbai M (2007) Exact retrospective Monte Carlo computation of arithmetic average Asian options. Monte Carlo Methods and Applications MCMA 13(2):135–171.Google Scholar
  • Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus (Springer-Verlag, New York).Google Scholar
  • Kohatsu-Higa A, Montero M (2004) Malliavin calculus in finance. Handbook of Computational and Numerical Methods in Finance (Birkhäuser, Boston), 111–174.CrossrefGoogle Scholar
  • Larguinho M, Dias JC, Braumann CA (2013) On the computation of option prices and Greeks under the CEV model. Quant. Finance 13(6):907–917.CrossrefGoogle Scholar
  • Linetsky V, Mendoza R (2010) Constant elasticity of variance (CEV) diffusion model. Encyclopedia of Quantitative Finance, Vol. I (John Wiley & Sons, West Sussex, UK), 328–334.CrossrefGoogle Scholar
  • Protter PE (2005) Stochastic Integration and Differential Equations, Vol. 21 (Springer Science & Business Media, New York).CrossrefGoogle Scholar
  • Reutenauer V, Tanré E (2008) Exact simulation of prices and Greeks: Application to CIR. Article soumis, https://hal.inria.fr/inria-00319139.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.