Page 564 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 564
DELING ROUGHNESS AND LONG-RANGE DEPENDENCE WITH FRACTIONAL
PROCESSES (MS-18)
This talk is based on article Azmoodeh, E., Sottinen, T., Tudor, C.A. et al. Integration-by-
parts characterizations of Gaussian processes. Collect. Math. (2020). https://doi.org/
10.1007/s13348-019-00278-x
On mixed fractional SDEs with discontinuous drift coefficient
Ercan Sönmez, ercan.soenmez@aau.at
University of Klagenfurt, Austria
We prove existence and uniqueness of the solution for a class of mixed fractional stochastic
differential equations with discontinuous drift driven by both standard and fractional Brownian
motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely con-
tinuous derivative and applicable to solutions of mixed fractional stochastic differential equa-
tions with Lipschitz coefficients, which plays a key role in our proof of existence and unique-
ness. The proof of such a formula is new and relies on showing the existence of a density of the
law under mild assumptions on the diffusion coefficient.
Prediction of missing functional data with memory
Lauri Viitasaari, lauri.viitasaari@aalto.fi
Aalto University School of Business, Finland
We consider optimal prediction of functional observations Xi = (Xti)t∈[0,1], i = 1, . . . , n that
are realisations of some Gaussian subordinated process. We assume that parts of the paths
are unobservable, and our aim is to fill in the missing information as accurately as possible.
One natural approach is to predict some missing value Xsk by using the information provided
by Xsi, i = k of those functions Xi for which Xsi is observed. However, under memory the
unobserved Xsk relies heavily on that particular functional observation Xk directly, and thus
applying other observations Xi may be missleading, even if they are drawn from the same
stochastic process. In this talk we present a novel approach for accurate prediction of missing
information Xsk that is based on applying combined information provided by the observed part
of the path Xk and the observed values Xsi, i = k.
Decomposition formula for rough Volterra stochastic volatility models
Josep Vives, josep.vives@ub.edu
Universitat de Barcelona, Spain
Coauthors: Raúl Merino, Jan Pospisil, Tomas Sobotka, Tommi Sottinen
The research presented in this paper provides an alternative option pricing approach for a class
of rough fractional stochastic volatility models. These models are increasingly popular between
academics and practitioners due to their surprising consistency with financial markets. How-
ever, they bring several challenges alongside. Most noticeably, even simple nonlinear financial
derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC)
simulations which are more computationally demanding than similar MC schemes for standard
562
PROCESSES (MS-18)
This talk is based on article Azmoodeh, E., Sottinen, T., Tudor, C.A. et al. Integration-by-
parts characterizations of Gaussian processes. Collect. Math. (2020). https://doi.org/
10.1007/s13348-019-00278-x
On mixed fractional SDEs with discontinuous drift coefficient
Ercan Sönmez, ercan.soenmez@aau.at
University of Klagenfurt, Austria
We prove existence and uniqueness of the solution for a class of mixed fractional stochastic
differential equations with discontinuous drift driven by both standard and fractional Brownian
motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely con-
tinuous derivative and applicable to solutions of mixed fractional stochastic differential equa-
tions with Lipschitz coefficients, which plays a key role in our proof of existence and unique-
ness. The proof of such a formula is new and relies on showing the existence of a density of the
law under mild assumptions on the diffusion coefficient.
Prediction of missing functional data with memory
Lauri Viitasaari, lauri.viitasaari@aalto.fi
Aalto University School of Business, Finland
We consider optimal prediction of functional observations Xi = (Xti)t∈[0,1], i = 1, . . . , n that
are realisations of some Gaussian subordinated process. We assume that parts of the paths
are unobservable, and our aim is to fill in the missing information as accurately as possible.
One natural approach is to predict some missing value Xsk by using the information provided
by Xsi, i = k of those functions Xi for which Xsi is observed. However, under memory the
unobserved Xsk relies heavily on that particular functional observation Xk directly, and thus
applying other observations Xi may be missleading, even if they are drawn from the same
stochastic process. In this talk we present a novel approach for accurate prediction of missing
information Xsk that is based on applying combined information provided by the observed part
of the path Xk and the observed values Xsi, i = k.
Decomposition formula for rough Volterra stochastic volatility models
Josep Vives, josep.vives@ub.edu
Universitat de Barcelona, Spain
Coauthors: Raúl Merino, Jan Pospisil, Tomas Sobotka, Tommi Sottinen
The research presented in this paper provides an alternative option pricing approach for a class
of rough fractional stochastic volatility models. These models are increasingly popular between
academics and practitioners due to their surprising consistency with financial markets. How-
ever, they bring several challenges alongside. Most noticeably, even simple nonlinear financial
derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC)
simulations which are more computationally demanding than similar MC schemes for standard
562
