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Simulation of Lévy-Driven models and its application in finance
1. | School of Management, Fudan University, Guoshun Road 670, Shanghai 200433, China, China, China |
References:
[1] |
O. E. Barndorff-Nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics, Journal Of The Royal Statistical Society, Series B, 63 (2001), 167-241. |
[2] |
J. Bertoin, "Lévy Processes," 2nd edition, Cambridge University Press, Cambridge, 1996. |
[3] |
P. Carr and L. Wu, Time-changed Lévy processes and option pricing, Journal of Financial Economics, 71 (2004), 113-141.
doi: 10.1016/S0304-405X(03)00171-5. |
[4] |
Z. Chen, L. Feng and X. Lin, Simulating Lévy processes from their characteristic functions and financial applications, ACM Transactions on Modeling and Computer Simulation, 22 (2012). |
[5] |
R. Cont and P. Tankov, "Financial Modelling with Jump Processes," Chapman & Hall/CRC, Boca Raton, Florida, 2004. |
[6] |
P. Glasserman, "Gradient Estimation via Perturbation Analysis," Kluwer Academic, Boston, 1991. |
[7] |
P. Glasserman, "Monte Carlo Methods in Financial Engineering," Springer, New York, 2004. |
[8] |
P. Glasserman and Z. Liu, Estimating Greeks in simulating Lévy-driven models, Journal of Computational Finance, 14 (2010), 3-56. |
[9] |
M. C. Fu and J. Q. Hu, "Conditional Monte Carlo: Gradient Estimation and Optimization Applications," Kluwer Academic, Boston, 1997. |
[10] |
M. C. Fu, Variance-Gamma and Monte Carlo, Advances in Mathematical Finance, (2007), 21-35. |
[11] |
P. W. Glynn, Likelihood ratio gradient estimation: An overview, Proceedings of the 1987 Winter Simulation Conference, (1987), 366-374. |
[12] |
Y. C. Ho and X. R. Cao, "Perturbation Analysis of Discrete Event Dynamic Systems," Kluwer Academic, Boston, 1991.
doi: 10.1007/978-1-4615-4024-3. |
[13] |
B. Mondelbrot, "The variation of certain speculative prices," The Journal of Business, 36 (1963), 394-419.
doi: 10.1086/294632. |
[14] |
Y. J. Peng, M. C. Fu and J. Q. Hu, Gradient-based simulated maximum likelihood estimation for Lévy-Driven Ornstein-Uhlenbeck stochastic volatility models, Working Paper, (2012). |
[15] |
K. I. Sato, "Lévy Processes and Infinitely Divisible Distributions," Cambridge University Press, Cambridge, 1999. |
[16] |
W. Schoutens, "Lévy Processes in Finance: Pricing Financial Derivatives," Wiley, New York, 2003. |
show all references
References:
[1] |
O. E. Barndorff-Nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics, Journal Of The Royal Statistical Society, Series B, 63 (2001), 167-241. |
[2] |
J. Bertoin, "Lévy Processes," 2nd edition, Cambridge University Press, Cambridge, 1996. |
[3] |
P. Carr and L. Wu, Time-changed Lévy processes and option pricing, Journal of Financial Economics, 71 (2004), 113-141.
doi: 10.1016/S0304-405X(03)00171-5. |
[4] |
Z. Chen, L. Feng and X. Lin, Simulating Lévy processes from their characteristic functions and financial applications, ACM Transactions on Modeling and Computer Simulation, 22 (2012). |
[5] |
R. Cont and P. Tankov, "Financial Modelling with Jump Processes," Chapman & Hall/CRC, Boca Raton, Florida, 2004. |
[6] |
P. Glasserman, "Gradient Estimation via Perturbation Analysis," Kluwer Academic, Boston, 1991. |
[7] |
P. Glasserman, "Monte Carlo Methods in Financial Engineering," Springer, New York, 2004. |
[8] |
P. Glasserman and Z. Liu, Estimating Greeks in simulating Lévy-driven models, Journal of Computational Finance, 14 (2010), 3-56. |
[9] |
M. C. Fu and J. Q. Hu, "Conditional Monte Carlo: Gradient Estimation and Optimization Applications," Kluwer Academic, Boston, 1997. |
[10] |
M. C. Fu, Variance-Gamma and Monte Carlo, Advances in Mathematical Finance, (2007), 21-35. |
[11] |
P. W. Glynn, Likelihood ratio gradient estimation: An overview, Proceedings of the 1987 Winter Simulation Conference, (1987), 366-374. |
[12] |
Y. C. Ho and X. R. Cao, "Perturbation Analysis of Discrete Event Dynamic Systems," Kluwer Academic, Boston, 1991.
doi: 10.1007/978-1-4615-4024-3. |
[13] |
B. Mondelbrot, "The variation of certain speculative prices," The Journal of Business, 36 (1963), 394-419.
doi: 10.1086/294632. |
[14] |
Y. J. Peng, M. C. Fu and J. Q. Hu, Gradient-based simulated maximum likelihood estimation for Lévy-Driven Ornstein-Uhlenbeck stochastic volatility models, Working Paper, (2012). |
[15] |
K. I. Sato, "Lévy Processes and Infinitely Divisible Distributions," Cambridge University Press, Cambridge, 1999. |
[16] |
W. Schoutens, "Lévy Processes in Finance: Pricing Financial Derivatives," Wiley, New York, 2003. |
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