Name
Abstract | ||
|---|---|---|
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the limit case of vanishing Hurst index H. The so-obtained logmodulated fractional Brownian motion (log-fBm) is a continuous Gaussian process even for H = 0. As a consequence, the resulting super-rough stochastic volatility models can be analyzed over the whole range 0 <= H < 1/2 without the need of further normalization. We obtain skew asymptotics of the form log(1/T)(-pT H 1/2) as T -> 0, H >= 0, so no flattening of the skew occurs as H -> 0. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/20M135902X | SIAM JOURNAL ON FINANCIAL MATHEMATICS |
Keywords | DocType | Volume |
rough volatility models, stochastic volatility, rough Bergomi model, implied skew, fractional Brownian motion, log Brownian motion | Journal | 12 |
Issue | ISSN | Citations |
3 | 1945-497X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christian Bayer | 1 | 0 | 0.68 |
| Fabian Andsem Harang | 2 | 0 | 0.34 |
| Paolo Pigato | 3 | 0 | 0.34 |