Notice bibliographique
Résumé
We, as humans, learn from our mistakes. Ultimately, we progress and grow, both as an individual and as a society. After the catastrophic recession period due to the sub-prime mortgage crisis in 2007, researchers and mathematicians began to look for answers about the massive damages done by the crisis. These events suggested that there must be some other factors that had hidden and needed to be accounted for in the previous prevailing models of our financial markets. As many different explanations arose, the main focus was to find a way to account for these more significant crises with some economically interpretable assumptions. The existence of different states or regimes in our financial market is one of the most acceptable ideas so far, as we tend to notice that the market has been switching between cycles of booms and recessions. This idea has triggered many studies on regime-switching models, but mostly with Markov regimes, as they are mathematically simple and relatively easy to solve. However, some of the assumptions made behind the Markov switching models have been questionable and unrealistic. For instance, Markov regimes imply that each one of them can switch to any other state no matter how long we have stayed in the current state. This is deviating from what we would expect, as we usually observe that the likelihood of recovery has some correlation with the recession’s age; the longer we stay in a recession, the harder for the market to recover. Thus, the primary purpose of this thesis is to find a better model with a better explanation. The introduction of semi-Markov markets intuitively has a time-varying propensity of regime changes using the conditional intensity matrix. In general, the semi-Markov switching models should be more in line with our financial market and generate better results when simulating financial derivatives prices. In this thesis, we will start by introducing some related definitions and theorems first. We will develop a semi-martingale representation for both the discrete-time semi-Markov chains and continuous-time semi-Markov processes, with some examples and applications. Then, we will construct the theoretical framework of a stochastic model under a semi-Markov regime-switching process driven by Lévy processes. The first step is to derive its Itô’s formula, as we need it to find the semi-closed form formulas for the characteristic function of log prices. Then, we will be developing the risk-neutral measure specific to our semi-Markov switching models. As some of us may already know, the Lévy driven regime-switching markets are incomplete, which means that there is more than one risk-neutral measure when pricing financial derivatives. When pricing a European-style option, since we already have the semi-closed form of the characteristic function for log asset prices, it allows us to use a Fourier transform method, first derived by Carr and Madan, namely the Fractional Fast Fourier Transform (FRFT) algorithm to obtain the estimated option prices. When comparing with Markov switching models, estimations and simulations show that the semi-Markov model performs better. It also offers more insight into the dynamics of market regimes, providing us with a better explanation of where the financial market is headed to next.
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,003 | 0,009 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,001 |
| Méta-épidémiologie (sens large) | 0,002 | 0,002 |
| Bibliométrie | 0,002 | 0,002 |
| Études des sciences et des technologies | 0,001 | 0,002 |
| Communication savante | 0,002 | 0,002 |
| Science ouverte | 0,001 | 0,002 |
| Intégrité de la recherche | 0,002 | 0,003 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,006 | 0,001 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».