Essays on Financial Economics and Econometrics
Open Access
- Author:
- Zhu, Shengbo
- Graduate Program:
- Economics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 22, 2020
- 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 - 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 - Abstract:
- 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 then use them to price other derivatives, which contributes to the literature of implied processes. In addition, it also shows that a multi-period arbitrage process can be reduced to a random vector. The theoretical contribution of this chapter is that it sheds new light on the nature of arbitrage processes and the Fundamental Theorem of Asset Pricing. Practically it provides a general framework to precisely extract the information contained in prices of frequently-traded derivatives and then price other derivatives. Chapter 3 derives the asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator constructed from a Markov hypothesis in the context of a dependent process without making assumptions about the functional form of the likelihood functions. Moreover, this chapter also examines the relation between the two asymptotic distributions and describes the conditions under which the asymptotic variance of the QMLE converges to that of the MLE when more and more lags are used in the construction of the QMLE.