10,448 research outputs found
Updating the Option Implied Probability of Default Methodology
In this paper we ‘update’ the option implied probability of default (option iPoD) approach
recently suggested in the literature. First, a numerically more stable objective function for
the estimation of the risk neutral density is derived whose integrals can be solved analytically.
Second, it is reasoned that the originally proposed approach for the estimation of the PoD
has some serious drawbacks and hence an alternative procedure is suggested that is based
on the Lagrange multipliers. Carrying out numerical evaluations and a practical application
we find that the framework provides very promising results
Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
Quantum algorithms have the potential to outperform their classical
counterparts in a variety of tasks. The realization of the advantage often
requires the ability to load classical data efficiently into quantum states.
However, the best known methods require gates to
load an exact representation of a generic data structure into an -qubit
state. This scaling can easily predominate the complexity of a quantum
algorithm and, thereby, impair potential quantum advantage. Our work presents a
hybrid quantum-classical algorithm for efficient, approximate quantum state
loading. More precisely, we use quantum Generative Adversarial Networks (qGANs)
to facilitate efficient learning and loading of generic probability
distributions -- implicitly given by data samples -- into quantum states.
Through the interplay of a quantum channel, such as a variational quantum
circuit, and a classical neural network, the qGAN can learn a representation of
the probability distribution underlying the data samples and load it into a
quantum state. The loading requires
gates and can, thus, enable the
use of potentially advantageous quantum algorithms, such as Quantum Amplitude
Estimation. We implement the qGAN distribution learning and loading method with
Qiskit and test it using a quantum simulation as well as actual quantum
processors provided by the IBM Q Experience. Furthermore, we employ quantum
simulation to demonstrate the use of the trained quantum channel in a quantum
finance application.Comment: 14 pages, 13 figure
The Futility of Utility: how market dynamics marginalize Adam Smith
Econometrics is based on the nonempiric notion of utility. Prices, dynamics,
and market equilibria are supposed to be derived from utility. Utility is
usually treated by economists as a price potential, other times utility rates
are treated as Lagrangians. Assumptions of integrability of Lagrangians and
dynamics are implicitly and uncritically made. In particular, economists assume
that price is the gradient of utility in equilibrium, but I show that price as
the gradient of utility is an integrability condition for the Hamiltonian
dynamics of an optimization problem in econometric control theory. One
consequence is that, in a nonintegrable dynamical system, price cannot be
expressed as a function of demand or supply variables. Another consequence is
that utility maximization does not describe equiulibrium. I point out that the
maximization of Gibbs entropy would describe equilibrium, if equilibrium could
be achieved, but equilibrium does not describe real markets. To emphasize the
inconsistency of the economists' notion of 'equilibrium', I discuss both
deterministic and stochastic dynamics of excess demand and observe that Adam
Smith's stabilizing hand is not to be found either in deterministic or
stochastic dynamical models of markets, nor in the observed motions of asset
prices. Evidence for stability of prices of assets in free markets simply has
not been found.Comment: 46 pages. accepte
Thermodynamic analogies in economics and finance: instability of markets
Interest in thermodynamic analogies in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper we go further and use a standard strategy from trading theory to pinpoint why thermodynamic analogies necessarily fail to describe financial markets, in spite of the presence of liquidity as the underlying basis for market entropy. Market liquidity of frequently traded assets does play the role of the ‘heat bath‘, as anticipated by von Neumann, but we are able to identify the no-arbitrage condition geometrically as an assumption of translational and rotational invariance rather than (as finance theorists would claim) an equilibrium condition. We then use the empirical market distribution to introduce an asset’s entropy and discuss the underlying reason why real financial markets cannot behave thermodynamically: financial markets are unstable, they do not approach statistical equilibrium, nor are there any available topological invariants on which to base a purely formal statistical mechanics. After discussing financial markets, we finally generalize our result by proposing that the idea of Adam Smith’s Invisible Hand is a falsifiable proposition: we suggest how to test nonfinancial markets empirically for the stabilizing action of The Invisible Hand.Economics; utility; entropy and disorder; thermodynamics; financial markets; stochastic processes;
Why Money Trickles Up - Wealth & Income Distributions
This paper combines ideas from classical economics and modern finance with
the general Lotka-Volterra models of Levy & Solomon to provide straightforward
explanations of wealth and income distributions. Using a simple and realistic
economic formulation, the distributions of both wealth and income are fully
explained. Both the power tail and the log-normal like body are fully captured.
It is of note that the full distribution, including the power law tail, is
created via the use of absolutely identical agents. It is further demonstrated
that a simple scheme of compulsory saving could eliminate poverty at little
cost to the taxpayer.Comment: 45 pages of text, 36 figure
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