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Penn State University

1. Zhu, Shengbo. Essays on Financial Economics and Econometrics.

Degree: 2020, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/18113szz126

In a recent seminal paper, Steve Ross proposed an attractive strategy to extract the physical distribution and risk aversion from just state prices. However, empirical papers that try to use his Recovery Theorem almost all lead to a depressing conclusion: the recovery theorem does not work. Both the state-price matrix and the recovered physical transition matrix are unreasonable and highly sensitive to subjective specifications and constraints. Borovička, Hansen and Scheinkman (2016) proposes a widely-accepted explanation for the empirical failure: according to the Hansen-Scheinkman decomposition established in Hansen and Scheinkman (2009), the assumption about the stochastic discount factor in Ross (2015) is equivalent to arbitrarily setting the martingale component to be 1, which is quite unlikely in reality. In Chapter 1, I argue that in contrast to Borovička, Hansen and Scheinkman (2016), the assumption about the stochastic discount factor in Ross (2015) actually does not set the martingale component in the Hansen-Scheinkman decomposition to be 1. What causes the empirical failure is actually a time-homogeneous state-price matrix, which induces quite restrictive implications on the underlying price process and those restrictions are easily violated in reality. In particular, when the underlying price is used as the state variable or as one component
of the state vector, this restriction becomes an eigenvalue equation that contradicts the important eigenvalue equation in Ross (2015), which in this case makes the Recovery Theorem not just empirically implausible, but also logically inconsistent.
Chapter 2 studies the following conceptual question: in what sense is the Fundamental Theorem of Asset Pricing similar to the two-period no-arbitrage theorem (a.k.a., Farkas lemma)? The purpose of studying this question is (1) to study the information that can be extracted from prices of derivatives in a multi-period context, generalizing the result in a two-period case in Breeden and Litzenberger (1978); (2) to find a way
to write down explicitly a multi-period arbitrage process, just as a two-period arbitrage can be written down as a vector. To answer the above conceptual question, I break it down into three more specific questions: (1) How to generalize the concept of states to a multi-period model? (2) How to generalize the concept of state price to a multi-period model? (3) In what sense is a multi-period arbitrage process similar to a two-period arbitrage strategy which is just a vector? The key to answering those questions is to explicitly describe the probability space on which price processes are defined, especially what “information flow” means. I adopt
the canonical probability space (i.e., the space of all possible paths of some price process) and propose to consider the whole path of as the state variable and the “path prices”(i.e., the equivalent martingale measure) as the analogue of state prices. This chapter discusses how we can recover prices of paths using prices of associated derivative securities and…
*Advisors/Committee Members: Andrew Ronald Gallant, Dissertation Advisor/Co-Advisor, Andrew Ronald Gallant, Committee Chair/Co-Chair, Patrik Guggenberger, Committee Member, Keisuke Hirano, Committee Member, Jingzhi Huang, Outside Member, Shouyong Shi, Committee Member, Marc Albert Henry, Program Head/Chair.*

Subjects/Keywords: Ross recovery theorem; equivalent martingale measure; stochastic discount factor; martingale condition; state price; path price; intrinsic inconsistency; implied process; fundamental theorem of asset pricing; canonical probability space; Markovian quasi-MLE; conditional asymptotic independence; mixing condition; near-epoch dependence

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APA (6^{th} Edition):

Zhu, S. (2020). Essays on Financial Economics and Econometrics. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/18113szz126

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Zhu, Shengbo. “Essays on Financial Economics and Econometrics.” 2020. Thesis, Penn State University. Accessed November 28, 2020. https://submit-etda.libraries.psu.edu/catalog/18113szz126.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Zhu, Shengbo. “Essays on Financial Economics and Econometrics.” 2020. Web. 28 Nov 2020.

Vancouver:

Zhu S. Essays on Financial Economics and Econometrics. [Internet] [Thesis]. Penn State University; 2020. [cited 2020 Nov 28]. Available from: https://submit-etda.libraries.psu.edu/catalog/18113szz126.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhu S. Essays on Financial Economics and Econometrics. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/18113szz126

Not specified: Masters Thesis or Doctoral Dissertation