Price Variations in a Stock Market With Many Agents

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between ``rational'' traders whose behavior is derived from fundamental analysis of the stock, including dividends, and ``noise traders'', whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, ``bubbles'' often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted to J. Math. Eco

Derivatives and Default Risk

Upstream producers that possess market power, sell forwards with a lengthy duration to regional electricity companies (REC). As part of the liberalization of the electricity market, RECs have been privatized and exposed to a possible bankruptcy threat if spot prices have fallen below their expected value. The downstream firms’ expected profit is larger, when it is less likely to be bailed out, the effect on upstream profits is ambiguous while consumers loose. Options are less welfare increasing than forwards, but the difference is minimal. In the presence of bankruptcy, options are the preferred welfare maximizing market instrument

Derivatives and Default Risk

Upstream producers that possess market power, sell forwards with a lengthy duration to regional electricity companies (REC). As part of the liberalization of the electricity market, RECs have been privatized and exposed to a possible bankruptcy threat if spot prices have fallen below their expected value. The downstream firms’ expected profit is larger, when it is less likely to be bailed out, the effect on upstream profits is ambiguous while consumers loose. Options are less welfare increasing than forwards, but the difference is minimal. In the presence of bankruptcy, options are the preferred welfare maximizing market instrument.Forwards; Options; Default Risk; Market Efficiency

The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Bequest and Precautionary Motives

Strong bequest motives can explain low retirement spending, but so equally can strong precautionary motives. Given this identification problem, the recent tradition has been largely to ignore bequest motives. We develop a rich model of spending in retirement that allows for both motives, and introduce a "Medicaid aversion" parameter that plays a key role in determining precautionary savings. We implement a "strategic" survey to resolve the identification problem between bequest and precautionary motives. We find that strong bequest motives are too prevalent to be ignored. Moreover, Medicaid aversion is widespread, and helps explain the low spending of many middle class retirees.

A Network Model of Super-systemic Crises

Although the financial systems of advanced countries have weathered numerous shocks in recent years, the events triggered by the sub-prime crisis of August 2007 have been “super-systemic” in scope, enveloping financial institutions across the major economies as well as far away Iceland and New Zealand. In this paper, we apply network techniques to develop a framework for analyzing financial contagion that isolate the probability of contagion from its potential spread. Our results suggest that complex financial systems may be robust-yet-fragile in nature. Under plausible assumptions, the greater connectivity implied by new financial instruments (e.g., credit derivatives) reduces the likelihood of contagion. But the impact on the financial system, in the event of problems, can be on a significantly larger scale than before.

Innovation and Equilibrium?

A discussion is given of the problems involved in the formal modeling of the innovation process. The link between innovation and finance is stressed. The nature of how the circular flow of funds is broken and the role of finance in evaluation and control is discussed.Innovation, Invention, Circular flow, Finance

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Speeding Up MCMC by Efficient Data Subsampling

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to $n$ and $m$, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small $m$ in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.Comment: Main changes: The theory has been significantly revise