Results 1  10
of
57
New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model
 Journal of Business
, 1998
"... We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black ..."
Abstract

Cited by 80 (7 self)
 Add to MetaCart
We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical BlackScholes model. We study implicit volatilities, the smile effect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit riskneutral density function from option data. Finally we present some new valueat risk calculations leading to new perspectives to cope with model risk. I Introduction There is little doubt that the BlackScholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...
Pathological Outcomes of Observational Learning
 ECONOMETRICA
, 1999
"... This paper explores how Bayesrational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may typespecific `herds' eventually arise, but a new robust possibility emerges: confounded learning. ..."
Abstract

Cited by 51 (2 self)
 Add to MetaCart
This paper explores how Bayesrational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may typespecific `herds' eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history oers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identied limit outcomes do arise, we exploit the Markovmartingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.
What Matters in Neuronal Locking?
"... Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessa ..."
Abstract

Cited by 46 (10 self)
 Add to MetaCart
Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1
Ergodic Theory on GaltonWatson Trees: Speed of Random Walk and Dimension of Harmonic Measure
 Systems
, 1994
"... . We consider simple random walk on the family tree T of a nondegenerate supercritical GaltonWatson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of T . Concretely, this implies that an exponentially smal ..."
Abstract

Cited by 40 (12 self)
 Add to MetaCart
. We consider simple random walk on the family tree T of a nondegenerate supercritical GaltonWatson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of T . Concretely, this implies that an exponentially small fraction of the nth level of T carries most of the harmonic measure. First order asymptotics for the rate of escape, Green function and the Avez entropy of the random walk are also determined. Ergodic theory of the shift on the space of random walk paths on trees is the main tool; the key observation is that iterating the transformation induced from this shift to the subset of "exit points" yields a nonintersecting path sampled from harmonic measure. x1. Introduction. Consider a supercritical GaltonWatson branching process with generating function f(s) = P 1 k=0 p k s k , i.e., each individual has k offspring with probability p k , and m := f 0 (1) ? 1. Started with a single prog...
Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals
 Journal of Economic Theory
, 1992
"... Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitic ..."
Abstract

Cited by 31 (0 self)
 Add to MetaCart
Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitication for such an approximation is that the population is assumed to be very large and thus some law of large numbers must hold. This paper gives a characterization of random matching schemes for countably infinite populations. In particular this paper shows that there exists a random matching scheme such that the stochastic system and the deterministic system are the same. Journal of Economic Literature Classification
Why Some Fitness Landscapes are Fractal
, 1993
"... Many biological and biochemical measurements, e.g. the "fitness" of a particular genome, or the binding affinity to a particular substrate, can be treated as a "fitness landscape", an assignment of numerical values to points in sequence space (or some other configuration space). As an alternative to ..."
Abstract

Cited by 21 (11 self)
 Add to MetaCart
Many biological and biochemical measurements, e.g. the "fitness" of a particular genome, or the binding affinity to a particular substrate, can be treated as a "fitness landscape", an assignment of numerical values to points in sequence space (or some other configuration space). As an alternative to the enormous amount of data required to completely describe such a landscape, we propose a statistical characterization, based on the properties of a random walk through the landscape, and, more specifically, its autocorrelation function. Under assumptions roughly satisfied by two classes of simple model landscapes (the Nk model and the pspin model) and by the landscape of estimated free energies of RNA secondary structures, this autocorrelation function, along with the mean and variance of individual points and the size of the landscape, completely characterize it. Having noted that these and other landscapes of estimated replication and degradation rates all have a well defined correlat...
Market research and market design
 Advances in Theoretical Economics
, 2003
"... be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress. Advances in Theoretical Economics is one of The B.E. ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress. Advances in Theoretical Economics is one of The B.E.
When Is The Student tStatistic Asymptotically Standard Normal?
, 1996
"... Let X; X i ; i2N, be independent identically distributed random variables. It is shown that the Student tstatistic based upon the sample fX i g n i=1 is asymptotically N(0;1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the selfnormali ..."
Abstract

Cited by 19 (3 self)
 Add to MetaCart
Let X; X i ; i2N, be independent identically distributed random variables. It is shown that the Student tstatistic based upon the sample fX i g n i=1 is asymptotically N(0;1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the selfnormalized sums Un:= P n i=1 X i ffi\Gamma P n i=1 X 2 i \Delta 1=2 ; n2N, are stochastically bounded then they are uniformly subgaussian that is, sup n E exp(U 2 n )!1 for some ?0.
Fast Simulation of Packet Loss Rates in a Shared Buffer Communications Switch
 ACM Transactions on Modeling and Computer Simulation
, 2001
"... This paper describes an efficient technique for estimating, via simulation, the probability of buffer overows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
This paper describes an efficient technique for estimating, via simulation, the probability of buffer overows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity.