Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff
Giles (Oper. Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational...
| المؤلفون الرئيسيون: | , , |
|---|---|
| التنسيق: | Journal article |
| اللغة: | English |
| منشور في: |
2009
|
| الملخص: | Giles (Oper. Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational complexity of standard Monte Carlo. Giles analysed globally Lipschitz payoffs, but also found good performance in practice for non-globally Lipschitz cases. In this work, we show that the multi-level Monte Carlo method can be rigorously justified for non-globally Lipschitz payoffs. In particular, we consider digital, lookback and barrier options. This requires non-standard strong convergence analysis of the Euler-Maruyama method. © Springer-Verlag 2009. |
|---|