Statistical romberg extrapolation: A new variance reduction method and applications to option pricing

Annals of Applied Probability

Volumn 15, Issue 4, 2005, Pages 2681-2705

  Kebaier, Ahmed ^a,b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b UFR des Sciences et Technologie   (France)

Author keywords

Central limit theorem; Finance; Monte Carlo simulation; Option pricing; Romberg extrapolation; Variance reduction

Indexed keywords

EID: 30844448318     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051605000000511     Document Type: Article

References (17)

1. ALDOUS, D. J. and EAGLESON, G. K. (1978). On mixing and stability of limit theorems. Ann. Probab. 6 325-331. MRS17416
2. BALLY, V. and TALAY, D. (1996). The law of the Euler scheme for stochastic differential equations. I. Convergence rate of the distribution function. Probab. Theory Related Fields 10443-60. MR1367666
3. BOYLE, P., BROADIE, M. and GLASSERMAN, P. (1997). Monte Carlo methods for security pricing. J. Econom. Dynam. Contml 21 1267-1321. MR1470283
4. BROADIE, M. and DETEMPLE, J. (1997). Recent advances in numerical methods for pricing derivative securities. In Numerical Methods in Finance 43-66. Cambridge Univ. Press. MR 1470508
5. DUFRE, D. and GLYNN, P. (1995). Efficient Monte Carlo simulation of security prices. Ann. Appl. Probab. 5 897-905. MR1384358
6. FAURE, O. (1992). Simulation du mouvement Brownien et des diffusions. Ph.D. thesis, Ecole Nationale des Ponts et Chaussées.
7. JACOD, J. (1997). On continuous conditional Gaussian martingales and stable convergence in law. Séminaire de Probabilités XXXI. Lecture Notes in Math. 1655 232-246. Springer, Berlin. MR1478732
8. JACOD, J., KURTZ, T. G., MÉLÉARD, S. and PROTTER, P. (2005). The approximate Euler method for Levy driven stochastic differential equations. Ann. Inst. H. Poincaré. Special Issue Devoted to the Memory of P. A. Meyer 41 523-558. MR2139032
9. JACOD, J. and PROTTER, P. (1998). Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 267-307. MR1617049
10. KEBAIER, A. (2004). Romberg extrapolation, variance reduction and applications to option pricing. Preprint.
11. KURTZ, T. G. and PROTTER, P. (1991). Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs. In Stochastic Analysis 331-346. Academic Press, Boston, MA. MR1119837
12. KURTZ, T. G. and PROTTER, P. (1999). Weak error estimates for simulation schemes for SDEs.
13. LAMBERTON, D. and LAPEYRE, B. (1997). Introduction au calcul stochastique appliqué à la finance, 2nd ed. Ellipses, Paris. MR1607509
14. PROTTER, P. (1990). Stochastic Integration and Differential Equations. Springer, Berlin. MR 1037262
15. RÉNYI, A. (1963). On stable sequences of events. Sankhyā Ser. A 25 293-302. MR170385
16. TALAY, D. and TUBARO, L. (1990). Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 483-509. MR1091544
17. TEMAM, E. (2001). Couverture approché d'options exotiques. Pricing des options Asiatiques. Ph.D. thesis, Univ. Paris VI.