dc.date.accessioned | 2022-12-28T12:21:38Z | |
dc.date.available | 2022-12-28T12:21:38Z | |
dc.date.issued | 2022 | |
dc.identifier.uri | http://hdl.handle.net/10852/98381 | |
dc.description.abstract | Financial markets have extremely complex behavior that cannot be fully modeled using classical approaches. In particular, numerous empirical studies show that market volatility exhibits some form of long-range dependence and has time-varying Hölder regularity with prominent periods of “roughness” (i.e. of Hölder order ≈0.1). These two properties are far beyond the capabilities of classical Brownian diffusions and it is challenging to reproduce them simultaneously in one model.
In the present thesis, we suggest a novel volatility modeling framework that grasps this unconventional behavior and solves a number of technical problems that are typical for classical stochastic volatility models. Namely, our model comprises the following properties:
- flexibility in the noise: the suggested model accepts various drivers – from fractional Brownian motions with different Hurst indices to general Hölder continuous processes – to account for different option pricing phenomenons;
- control over the moments of the price: the model ensures the existence of moments of necessary orders for the corresponding price process;
- positivity: the volatility process is strictly positive and has inverse moments to ensure reasonable behavior of martingale densities.
We also present a variety of associated numerical methods and propose practically feasible algorithms for various applications, such as the pricing of contingent claims (including options with discontinuous payoffs) and mean-square hedging. | en_US |
dc.language.iso | en | en_US |
dc.relation.haspart | Paper I. Mishura, Yu., Yurchenko-Tytarenko, A. “Standard and fractional reflected Ornstein-Uhlenbeck processes as the limits of square roots of Cox-Ingersoll-Ross processes”. Stochastics, 2022. An author version is included in the thesis. The published version is available at: https://doi.org/10.1080/17442508.2022.2047188 | |
dc.relation.haspart | Paper II. Di Nunno, G., Mishura, Yu., Yurchenko-Tytarenko, A. “Sandwiched SDEs with unbounded drift driven by Hölder noises”. To appear in Advances in Applied Probability 55(3), 2023. arXiv: 2012.11465. To be published. The paper is removed from the thesis in DUO awaiting publishing. | |
dc.relation.haspart | Paper III. Di Nunno, G., Mishura, Yu., Yurchenko-Tytarenko, A. “Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises”. Numerical Algorithms, 2022. An author version is included in the thesis. The published version is available at: https://doi.org/10.1007/s11075-022-01424-6 | |
dc.relation.haspart | Paper IV. Di Nunno, G., Mishura, Yu. , Yurchenko-Tytarenko, A. “Option pricing in Sandwiched Volterra Volatility model”. Submitted for publication. arXiv: 2209.10688. To be published. The paper is removed from the thesis in DUO awaiting publishing. | |
dc.relation.haspart | Paper V. Di Nunno, G., Yurchenko-Tytarenko, A. “Sandwiched Volterra Volatility model: Markovian approximations and hedging”. Submitted for publication. arXiv: 2209.13054. To be published. The paper is removed from the thesis in DUO awaiting publishing. | |
dc.relation.uri | https://doi.org/10.1080/17442508.2022.2047188 | |
dc.relation.uri | https://doi.org/10.1007/s11075-022-01424-6 | |
dc.title | Stochastic Volterra volatility models | en_US |
dc.type | Doctoral thesis | en_US |
dc.creator.author | Yurchenko-Tytarenko, Anton | |
dc.type.document | Doktoravhandling | en_US |