A Partially-Observed Merton’s Model for Financial Ultra-High Frequency (UHF) Data with Bayesian Learning via Filtering Equations
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| Publicado en: | ProQuest Dissertations and Theses (2025) |
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| 100 | 1 | |a Kridan, Jamila | |
| 245 | 1 | |a A Partially-Observed Merton’s Model for Financial Ultra-High Frequency (UHF) Data with Bayesian Learning via Filtering Equations | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a This dissertation proposes a new model, referred to as a partially observed Merton model, for financial ultra-high-frequency data. The model is built upon the classical Merton model, which extends the Black-Scholes model by incorporating a jump component to account for abnormal price fluctuations. Both Merton model and Black-Scholes model are widely used in financial economics.The partially observed Merton’s model is constructed to match two features in ultrahigh-frequency (UHF) data: random trading times and trading noises. We develop a Bayesian framework for estimating model parameters and for model selection between two partially observed models. We employ the Bayesian inference, including estimation and model selection, via filtering equations approach to construct efficient recursive algorithms for parameter and model uncertainty quantification.Specifically, adding the jump component in Merton model significantly complicates the related filtering equations, which are stochastic PDEs (SPDEs) that govern the evaluation of the joint posterior and the Bayes Factors. To numerically solve the SPDEs so as to quantify parameter and model uncertainty as data stream in, we apply the related weak convergence theorems, enabling the use of the Markov chain approximation method to construct consistent recursive algorithms via explicit and implicit methods. Due to the positivity of the measure masses, the explicit algorithm suffers from the curse of fine step size. We construct the implicit recursive algorithms involving the iterated Thomas algorithm to overcome the fine-step-size curse and significantly mitigate the computation costs. The implicit recursive algorithms are consistent, easily parallelized, and efficient, with the potential for real-time parameter and model learning. We prove the nonnegativityand convergence of the iterated Thomas algorithm, develop related computer programs, and present preliminary simulation studies. | |
| 653 | |a Statistics | ||
| 653 | |a Bioinformatics | ||
| 653 | |a Finance | ||
| 653 | |a Information science | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3244288924/abstract/embedded/H09TXR3UUZB2ISDL?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3244288924/fulltextPDF/embedded/H09TXR3UUZB2ISDL?source=fedsrch |