Abstract
Giles (Multilevel Monte Carlo path simulation Operations Research, 2008; 56:607-617) 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 payff 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 justifed 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.
| Original language | English |
|---|---|
| Pages (from-to) | 403-413 |
| Number of pages | 10 |
| Journal | Finance and Stochastics |
| Volume | 13 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sep 2009 |
Keywords
- barrier option
- complexity
- digital option
- Euler-Maruyama
- lookback option
- path
- dependent option
- statistical error
- strong error
- weak error
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Giles, M. B., Higham, D. J., & Mao, X. (2009). Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Finance and Stochastics, 13(3), 403-413. https://doi.org/10.1007/s00780-009-0092-1