A Study of Option Pricing Models – Lognormal or Hyperbolic Levy ? By Chen Chen This paper is an investigation into two option pricing models: widely-used Black-Scholes model and one of its augmented extensions – hyperbolic Levy model. Firstly, we have a detailed discussion about the celebrated Black-Scholes model. However, clearly there are many deficiencies in Black-Scholes assumptions. In ord...

We conduct a statistical study of human mobility using over 1000 hours of GPS traces of human walks involving 44 participants in five different locations, two university campuses, state fair, New York City, and Disney World. Our data reveals statistical features similar to those in what physicists have long called Levy random walks (or Levy walks). These features include heavy-tail distribution...

Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a ‘mes...

In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices. This enables us to generate an implicit volatility surface implied by market data. This model is of particular interest since it extends the seminal Black Sc...

Mitochondrial dysfunction is involved in many neurodegenerative disorders in humans. Here we report mutations in a gene (designated levy) that codes for subunit VIa of cytochrome c oxidase (COX). The mutations were identified by the phenotype of temperature-induced paralysis and showed the additional phenotypes of decreased COX activity, age-dependent bang-induced paralysis, progressive neurode...

[1] We analyze Surface Stereo Imager observations of rocks, sediments, and permafrost-related landforms in the vicinity of the Phoenix lander, comparing the imaged features to analogous examples of physical weathering and periglacial processes observed in the Antarctic Dry Valleys. Observations at the Phoenix landing site of pitted rocks, ‘‘puzzle rocks’’ undergoing in-situ breakdown, perched c...

Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are d...

In this book, David Benatar argues that every person is severely harmed by being brought into existence, and that in bringing any person into existence one impermissibly harms that person. His conclusion is not merely that by bringing a person into existence, one harms him. That claim is compatible with the claim that by bringing a person into existence, one also greatly benefits him, and even ...