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80
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 ..."
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Cited by 135 (7 self)
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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 learn ..."
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Cited by 109 (3 self)
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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.
Ergodic theory on Galton–Watson trees: speed of random walk and dimension of harmonic measure. Ergodic Theory Dynam
 Systems
, 1995
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Bayesian Learning in Social Networks
, 2010
"... We study the (perfect Bayesian) equilibrium of a model of learning over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochasticallygenerated neighborhood of individuals, and chooses one of two possible actions. T ..."
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Cited by 52 (9 self)
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We study the (perfect Bayesian) equilibrium of a model of learning over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochasticallygenerated neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). We characterize purestrategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning—convergence (in probability) to the right action as the social network becomes large. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of “expansion in observations”. We also characterize conditions under which there will be asymptotic learning when private beliefs are bounded.
Menu costs and the neutrality of money
 Quarterly Journal of Economics CII
, 1987
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 50 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
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 ..."
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Cited by 48 (10 self)
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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
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 ..."
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Cited by 48 (0 self)
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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
2004), Equilibria in financial markets with heterogeneous agents: A probabilistic perspective
 J. Math. Econ
"... We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and th ..."
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Cited by 28 (3 self)
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We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are “chartist ” or extrapolatory rules. Prices can exhibit transient behaviour when chartists predominate. However, if the probability that an agent will switch to being a “chartist ” is not too high then the process does not explode. There are occasional bubbles but they inevitably burst. In fact, we prove that the limit distribution of the price process exists and is unique. This limit distribution may be thought of as the appropriate equilibrium notion for such markets. A number of characteristics of financial time series can be captured by this sort of model. In particular, the presence of chartists fattens the tails of the stationary distribution. JEL subject classification: C62,D84,G12 Key words: financial markets, stochastic price processes, limit distributions, forecasting rules