Method | Structure | Error | Complexity |
Cholesky | Static | 0 | |
Hosking, Dieker [28,17] | Recursive | 0 | |
Dietrich, Newsam [18] | Static | 0 | |
Bennedsen, Lunde, Pakkanen [12] | Recursive | ||
Carmona, Coutin, Montseny [15] | Recursive | ||
This paper | Recursive |
Many fractional processes can be represented as an integral over a family of Ornstein–Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also some limitations of such representations as the basis of Monte Carlo schemes for fractional volatility models such as the rough Bergomi model.
Citation: |
Figure 1.
Volterra Brownian motion of Hurst index
Figure 2.
Dependence of the approximations on the number
Figure 3.
The upper bound
Table 1.
Complexity of several numerical methods for sampling a fractional process
Method | Structure | Error | Complexity |
Cholesky | Static | 0 | |
Hosking, Dieker [28,17] | Recursive | 0 | |
Dietrich, Newsam [18] | Static | 0 | |
Bennedsen, Lunde, Pakkanen [12] | Recursive | ||
Carmona, Coutin, Montseny [15] | Recursive | ||
This paper | Recursive |
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