535 research outputs found
Essays in Risk Management and Asset Pricing with High Frequency Option Panels
The thesis investigates the information gains from high frequency equity option data with applications in risk management and empirical asset pricing. Chapter 1 provides the background and motivation of the thesis and outlines the key contributions. Chapter 2 describes the high frequency equity option data in detail. Chapter 3 reviews the theoretical treatments for Recovery Theorem. I derive the formulas for extracting risk neutral central moments from option prices in Chapter 4.
In Chapter 5, I specify a perturbation theory on the recovered discount factor, pricing kernel, and the physical probability density. In Chapter 6, a fast and fully-identified sequential programming algorithm is built to apply the Recovery Theorem in practice with noisy market data. I document new empirical evidence on the recovered physical probability distributions and empirical pricing kernels extracted from both index and single-name equity options. Finally, I build a left tail index from the recovered physical probability densities for the S&P 500 index options and show that the left tail index can be used as an indicator of market downside risk.
In Chapter 7, I uniquely introduce the higher dimensional option-implied average correlations and provide the procedures for estimating the higher dimensional option-implied average correlations from high frequency option data. In Chapter 8, I construct a market average correlation factor by sorting stocks according to their risk exposures to the option-implied average correlations. I find that (a) the market average correlation factor largely enhances the model-fitting of existing risk-adjusted asset pricing models. (b) the market average correlation factor yields persistent positive risk premiums in cross-sectional stock returns that cannot be explained by other existing risk factors and firm characteristic variables. Chapter 9 concludes the thesis
Metastability in a stochastic neural network modeled as a velocity jump Markov process
One of the major challenges in neuroscience is to determine how noise that is
present at the molecular and cellular levels affects dynamics and information
processing at the macroscopic level of synaptically coupled neuronal
populations. Often noise is incorprated into deterministic network models using
extrinsic noise sources. An alternative approach is to assume that noise arises
intrinsically as a collective population effect, which has led to a master
equation formulation of stochastic neural networks. In this paper we extend the
master equation formulation by introducing a stochastic model of neural
population dynamics in the form of a velocity jump Markov process. The latter
has the advantage of keeping track of synaptic processing as well as spiking
activity, and reduces to the neural master equation in a particular limit. The
population synaptic variables evolve according to piecewise deterministic
dynamics, which depends on population spiking activity. The latter is
characterised by a set of discrete stochastic variables evolving according to a
jump Markov process, with transition rates that depend on the synaptic
variables. We consider the particular problem of rare transitions between
metastable states of a network operating in a bistable regime in the
deterministic limit. Assuming that the synaptic dynamics is much slower than
the transitions between discrete spiking states, we use a WKB approximation and
singular perturbation theory to determine the mean first passage time to cross
the separatrix between the two metastable states. Such an analysis can also be
applied to other velocity jump Markov processes, including stochastic
voltage-gated ion channels and stochastic gene networks
A boundary integral formalism for stochastic ray tracing in billiards
Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain
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