On generating Monte Carlo samples of continuous diffusion bridges

Journal of the American Statistical Association

Volumn 105, Issue 490, 2010, Pages 820-838

  Lin, Ming ^a   Chen, Rong ^b,c   Mykland, Per ^d  

^a XIAMEN UNIVERSITY   (China)

^b RUTGERS UNIVERSITY   (United States)

^c Peking University   (China)

^d UNIVERSITY OF CHICAGO   (United States)

Author keywords

Backward pilot; Priority score; Resampling; Sequential Monte Carlo; Stochastic diffusion equation

Indexed keywords

EID: 78649397261     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2010.tm09057     Document Type: Article

References (25)

1. Aït-Sahalia, Y. (2004), "Disentangling Diffusion From Jumps," Journal of Financial Economics, 74, 487-528. [829]
2. Barndorff-Nielsen, O. E., and Shephard, N. (2002), "Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models," Journal of the Royal Statistical Society, Ser. B, 64, 253-280. [832]
3. Beskos, A., Papaspiliopoulos, O., Roberts, G., and Fearnhead, P. (2006), "Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes," Journal of Royal Statistical Society, Ser. B, 68, 333-382. [820,825,826,828]
4. Beskos, A., Roberts, G., Stuart, A., and Voss, J. (2008), "MCMC Methods for Diffusion Bridges," technical report, University of Warwick. [821]
5. Brandt,M.W., and Santa-Clara, P. (2002), "Simulated Likelihood Estimation of Diffusions With an Application to Exchange Rate Dynamics in Incomplete Markets," Journal of Financial Economics, 63, 61-210. [820,821]
6. Cox, J., Ross, S., and Rubinstein, M. (1979), "Option Pricing: A Simplified Approach," Journal of Financial Economics, 7, 229-263. [829]
7. Durham, G. B., and Gallant, A. R. (2002), "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, 20, 297-338. [820-823, 825-827,830,837]
8. Elerian, O., Chib, S., and Shephard, N. (2001), "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, 69, 959-993. [820-822]
9. Eraker, B. (2001), "MCMC Analysis of Diffusion Models With Application to Finance," Journal of Business & Economic Statistics, 19, 177-191. [820]
10. Gilks, W., Richardson, S., and Spiegelhalter, D. (1995), Markov Chain Monte Carlo in Practice, New York: Chapman & Hall. [821]
11. Hull, J., and White, A. (1987), "The Pricing of Options on Assets With Stochastic Volatilities," Journal of Finance, 42, 281-300. [832]
12. Kloeden, P., and Platen, E. (1992), Numerical Solution of Stochastic Differential Equations, Berlin: Springer-Verlag. [820]
13. Kong, A., Liu, J., and Wong, W. (1994), "Sequential Imputations and Bayesian Missing Data Problems," Journal of the American Statistical Association, 89, 278-288. [822]
14. Liu, J., and Chen, R. (1998), "Sequential Monte Carlo Methods for Dynamic Systems," Journal of the American Statistical Association, 93, 1032-1044. [822-824]
15. Liu, J. S. (1996), "Metropolized Independent Sampling With Comparisons to Rejection Sampling and Importance Sampling," Statistics and Compustion, 6, 113-119. [822]
16. -(2001), Monte Carlo Strategies in Scientific Computing, New York: Springer. [821,822]
17. Marshall, A. (1956), "The Use of Multi-Stage Sampling Schemes in Monte Carlo Computations," in Symposium on Monte Carlo Methods, ed. M. Meyer, New York: Wiley, pp. 123-140. [821]
18. Merton, R. C. (1976), "Option Pricing When Underlyinh Stock Returns Are Discontinous," Journal of Financial Economics, 3, 125-144. [829]
19. Pedersen, A. R. (1995), "Consistency and Asymptotic Normality of an Approximate Maximum Likelihood Estimator for Discretely Observed Diffusion Processes," Bernoulli, 1, 257-279. [820-822,830,833,837]
20. Pitt, M. K. (2002), "Smooth Particle Filters for Likelihood and Maximisation," technical report, University of Warwick. [828,837]
21. Robert, R., and Casella, G. (1999), Monte Carlo Statistical Methods, NewYork: Springer. [821]
22. Roberts, G. O., and Stramer, O. (2001), "On Inference for Partially Observed Nonlinear Diffusion Models Using the Metropolis-Hastings Algorithm," Biometrika, 88, 603-621. [820,821]
23. Shoji, I., and Ozaki, T. (1998), "Estimation for Nonlinear Stochastic Differential Equations by a Local Linearization Method," Stochastic Analysis and Applications, 16, 733-752. [821]
24. Stramer, O., and Yan, J. (2006), "On Simulated Likelihood of Discretely Observed Diffusion Processes and Comparison to Closed-Form Approximation," technical report, University of Iowa. [822]
25. Zhang, L., Mykland, P. A., and Aït-Sahalia, Y. (2005), "A Tale of Two Time Scales: Determining Integrated VolatilityWith Noisy High-Frequency Data," Journal of the American Statistical Association, 100, 1394-1411. [832]