Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff

Finance and Stochastics

Volumn 13, Issue 3, 2009, Pages 403-413

  Giles, Michael B ^a   Higham, Desmond J ^b   Mao, Xuerong ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Barrier option; Complexity; Digital option; Euler Maruyama; Lookback option; Path dependent option; Statistical error; Strong error; Weak error

Indexed keywords

EID: 70350634128     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-009-0092-1     Document Type: Article

References (11)

1. Avikainen, R.: Convergence rates for approximations of functionals of SDEs. Finance Stoch. (2007, to appear). arXiv:0712.3635v1.
2. Bally, V., Talay, D.: The law of the Euler scheme for stochastic differential equations (i): convergence rate of the distribution function. Probab. Theory Relat. Fields 104, 43-60 (1995).
3. Duffie, D., Glynn, P.: Efficient Monte Carlo simulation of security prices. Ann. Appl. Probab. 7, 325-348 (1995).
4. Giles, M.B.: Multi-level Monte Carlo path simulation. Oper. Res. 56, 607-617 (2008).
5. Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, Berlin (2004).
6. Gobet, E., Menozzi, S.: Discrete sampling of functionals of Itô processes. In: Séminaire de Probabilités XL, pp. 355-375. Springer, Berlin (2007).
7. Higham, D.J.: An Introduction to Financial Option Valuation: Mathematics, Stochastic and Computation. Cambridge University Press, Cambridge (2004).
8. Hull, J.C.: Options, Futures, & Other Derivatives, 4th edn. Prentice Hall, New Jersey (2000).
9. Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations, 3rd edn. Springer, Berlin (1999).
10. Mao, X.: Stochastic Differential Equations and Applications, 2nd edn. Horwood, Chichester (2007).
11. Müller-Gronbach, T.: The optimal uniform approximation of systems of stochastic differential equations. Ann. Appl. Probab. 12, 664-690 (2002).