Advances in data-driven financial econometrics and item response theory : theory and applications
Abstract/Contents
- Abstract
- Although option market is becoming increasingly important, its complex structure and abundant underlying assets make it very difficult to obtain relatively accurate pricing formulas or algorithms. The first part of this thesis focuses on a theoretical stochastic volatility model for option pricing. We propose a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that proposed model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution---a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar. The second part of this thesis gives a bias corrected algorithm of the least square Monte Carlo (LSM) algorithm for pricing American options. The traditional LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We also show that look-ahead bias is asymptotically proportional to the regressors-to-simulation paths ratio. Our findings are demonstrated with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. The LOOLSM method can be extended to other regression-based algorithms that improve the LSM method. In addition to option pricing, the third part of this thesis studies item response theory (IRT) and its application to foraging data analysis. A fundamental problem in biology is to understand how the differences among components, or variation in function, contribute to collective behavior. To tackle this problem, we first give a new approach to latent trait modeling in IRT, then design corresponding experiments and finally apply IRT to data analysis. We also give detailed explanation and further discussion for experiment results.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Liu, Chenru |
|---|---|
| Degree supervisor | Lai, T. L |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Blanchet, Jose H |
| Thesis advisor | Lu, Ying, 1960- |
| Degree committee member | Blanchet, Jose H |
| Degree committee member | Lu, Ying, 1960- |
| Associated with | Stanford University, Department of Management Science and Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Chenru Liu. |
|---|---|
| Note | Submitted to the Department of Management Science and Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/bn504hv7456 |
Access conditions
- Copyright
- © 2021 by Chenru Liu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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