Price Trajectories Research Articles

Investment under market and climate policy uncertainty

Climate change is considered as one of the major systematic risks for global society in the 21st century. Yet, serious efforts to slow the accumulation of emissions are still in their primordial stage and policy makers fail to give proper long-term signals to emitters. These days, investors do not only face uncertainty from volatile prices in the traditional markets, but also from the less conceivable uncertainty of stricter climate change policy. This paper investigates the impact of learning about the commitment of government to a climate policy regime in a real options framework. Two types of uncertainty are distinguished: market-driven price volatility around a mean price and bifurcating price trajectories mimicking uncertainty about changing policy regimes. One of the findings is that the producer facing market uncertainty about CO 2 prices invests into carbon-saving technology earlier than if the actual price path had been known on beforehand. This is not a typical real options outcome, but the result of optimizing under imperfect information, which leads to decisions that are different from the optimal strategies under full information. On the other hand, policy uncertainty induces the producer to wait and see whether the government will further commit to climate policy. This waiting is a real options effect. In other words, if learning about government commitment is more valuable than investing into mitigation technologies immediately, the option value exceeds the value of the technology and investment will be postponed. This might lead to supply shortages and limited diffusion of less carbon-intensive technology.

Traders' Expectations in Asset Markets: Experimental Evidence

We elicit traders' predictions of future price trajectories in repeated experimental markets for a 15-period-lived asset. We find that individuals' beliefs about prices are adaptive, and primarily based on past trends in the current and previous markets in which they have participated. Most traders do not anticipate market downturns the first time they participate in a market, and, when experienced, they typically overestimate the time remaining before market peaks and downturns occur. When prices deviate from fundamental values, belief data are informative to an observer in predicting the direction of future price movements and the timing of market peaks. (JEL C91, D12, D84, G11)

International passenger transport and climate change: A sector analysis in car demand and associated [formula omitted] emissions from 2000 to 2050

The paper provides global regionalized projections of passenger car demand, use and associated CO 2 emissions from 11 world regions. The study is based on empirical data that have been originally collated from international sources for the purpose of modeling region-specific car stock demand. Derived demands serve as indicator of car related fuel consumption and associated CO 2 emissions, which are calculated on the basis of behavioral and technological scenarios. The obtained CO 2 emission paths are sectoral baseline scenarios that identify region-specific potentials of growth in car induced CO 2 emissions assuming that current trends continue to prevail. The study adopts a multi-model approach to car demand by applying two methodologies rooted in the economics of consumption: utility maximization and single equation models. The utility maximization method for modeling car demand is driven by the preferences of the representative consumers of each world region, subject to exogenous price and income trajectories. The latter is adopted from an optimal growth model. This is a novel approach to projecting global regionalized sectoral car demands. The study is complemented by the application of single equation income–consumption models based on logistical Gompertz functions and non-linear regression techniques to compare model results.

Dynamic Bid Prices in Revenue Management

We formally derive the standard deterministic linear program (LP) for bid-price control by making an affine functional approximation to the optimal dynamic programming value function. This affine functional approximation gives rise to a new LP that yields tighter bounds than the standard LP. Whereas the standard LP computes static bid prices, our LP computes a time trajectory of bid prices. We show that there exist dynamic bid prices, optimal for the LP, that are individually monotone with respect to time. We provide a column generation procedure for solving the LP within a desired optimality tolerance, and present numerical results on computational and economic performance.

Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach

We use quantum mechanical methods to model the price dynamics in the financial market mathematically. We propose describing behavioral financial factors using the pilot-wave (Bohmian) model of quantum mechanics. The real price trajectories are determined (via the financial analogue of the second Newton law) by two financial potentials: the classical-like potential V (q) (“hard” market conditions) and the quantumlike potential U(q) (behavioral market conditions).

Application of Bohmian Mechanics to Dynamics of Prices of Shares: Stochastic Model of Bohm–Vigier from Properties of Price Trajectories

We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Through comparing properties of trajectories we come to the conclusion that the only possibility to proceed with real financial data is to apply the stochastic version of the pilot wave theory—the model of Bohm–Vigier.

Toward quantum-like modeling of financial processes

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ("hard" market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).

An analysis of capacity and price trajectories for the Ontario electricity market using dynamic Nash equilibrium under uncertainty

This paper studies investments in the Ontario Electricity Market which is currently being restructured. Our methodology is based on the concept of S-adapted open-loop Nash equilibrium. We examine the evolution of capital investments and pricing behavior of suppliers as uncertain electricity demand evolves over time (in Ontario). This study is particularly interesting since we compare the implications of two policies: (i) the current setting in which Ontario Power Generation (OPG) retains its generation units; (ii) the policy (set up in 2003) that required the divestiture of the largest supplier, OPG, and aimed to increase the number of independent suppliers in Ontario. We mainly focus on the independent generators like Bruce Nuclear. We use the tools of Stochastic Programming to compute the S-adapted open-loop Nash equilibrium market outcomes. We find that in the three-player market total capacity installation and market prices are higher than the ones in the five-player market. That is higher capacity may not necessarily alleviate exercise of market power. We also confirm the prediction by the National Energy Board that in a market with five major players, OPG's market share may reduce to a percentage between 35% and 40%.

A multi-parameter regularization approach for estimating parameters in jump diffusion processes

In this paper, we consider the inverse problem of estimating simultaneously the five parameters of a jump diffusion process based on return observations of a price trajectory. We show that there occur some ill-posedness phenomena in the parameter estimation problem, because the forward operator fails to be injective and small perturbations in the data may lead to large changes in the solution. We illustrate the instability effect by a numerical case study. To obtain stable approximate solutions of the estimation problem, we use a multi-parameter regularization approach, where a least-squares fitting of empirical densities is superposed by a quadratic penalty term of fitted semi-invariants with weights. A little number of required weights is controlled by a discrepancy principle. For the realization of this control, we propose and justify a fixed point iteration, where an exponent can be chosen arbitrarily positive. A numerical case study completing the paper shows that the approach provides satisfactory results and that the amount of computation can be reduced by an appropriate choice of the free exponent.

Quantum Bohmian model for financial market

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V ( q ) , where q = ( q 1 , … , q n ) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V ( q ) (“hard” market conditions) and quantum-like U ( q ) (behavioral market conditions).

Metaphors and the market: Consequences and preconditions of agent and object metaphors in stock market commentary

We investigated two types of metaphors in stock market commentary. Agent metaphors describe price trajectories as volitional actions, whereas object metaphors describe them as movements of inanimate objects. Study 1 examined the consequences of commentators’ metaphors for their investor audience. Agent metaphors, compared with object metaphors and non-metaphoric descriptions, caused investors to expect price trend continuance. The remaining studies examined preconditions, the features of a price trend that evoke agent vs. object metaphors. We hypothesized that the rate of agentic metaphors would depend on the trend direction (upday vs. downday) and steadiness (steady vs. unsteady). Two archival studies tracked the metaphoric content in end-of-day CNBC commentary as a function of daily price trajectories. As predicted, agent metaphors occurred more frequently on updays than downdays and especially so when the trends were relatively steady as opposed to unsteady. This held for both bull (Study 2) and bear market periods (Study 3). Study 4 replicated these findings in a laboratory experiment where participants took the role of stock market commentator.

Dynamic Pricing of Network Goods with Boundedly Rational Consumers

We present a model of dynamic monopoly pricing for a good that displaysnetwork effects. In contrast with the standard notion of arational-expectations equilibrium, we model consumers as boundedlyrational, and unable either to pay immediate attention to each pricechange, or to make accurate forecasts of the adoption of the networkgood. Our analysis shows that the seller's optimal price trajectory hasthe following structure: the price is low when the user base is below atarget level, is high when the user base is above the target, and is setto keep user base stationary once the target level has been attained. Weshow that this pricing policy is robust to a number of extensions, whichinclude the product's user base evolving over time, and consumers basingtheir choices on a mixture of a myopic and a stubbornexpectation of adoption. Our results differ significantly from thosethat would be predicted by a model based on rational-expectationsequilibrium, and are more consistent with the pricing of network goodsobserved in practice.

Measuring the Importance of the Uniform Nonsynchronization Hypothesis

In this paper we critically reappraise some measures of the importance of time-dependent price setting rules and propose an alternative way to gauge the significance of this type of price setting behaviour. The merits of the proposed measure are highlighted in an application using micro-data. Our results suggest that a large proportion of price trajectories may be compatible with simple time-dependent price setting mechanisms but the strength of this evidence very much depends on the way that is used to evaluate the importance of this type of behaviour.

OPTIMAL CONTINGENT CLAIMS AND CONSUMPTION

In complete financial markets, given a particular market variable, which could be finite dimensional (e.g., a price vector of a collection of stocks) or infinite dimensional (e.g., a price trajectory of some security over some period of time), the unique optimal strategy of consumption and investment in European claims contingent on that variable is obtained from two kinds of preference structure. Several examples are given to illustrate the optimality of the strategy. Results obtained in this paper are an extension of Jankunas [4].

Cohort Effects, Differential Accumulation and Hong Kong's Volatile Housing Market

As in much of east Asia, the past few decades have seen extraordinary rates of house price inflation in Hong Kong. After a relatively modest downturn in the early 1980s, prices rose rapidly until the Asian financial crisis in 1997. Since then, and despite increased government efforts to stimulate the stagnant property market, prices have continued to fall and negative equity remains pervasive. Given the centrality of property investment and speculation historically for households, financial institutions and for wider government economic strategies, the state of the residential market remains of central political and policy concern. Against this background of Hong Kong's apparently declining economic fortunes and major shifts in housing policy, this paper explores aspects of wealth accumulation in the home-ownership sector. Linking to a well-established set of debates in the academic literature, the paper explores the impact of policy change and house price trajectories on different cohorts of households. For example, those cohorts who entered home-ownership in the late 1980s generally saw rapid increases in their property values fuelled by generous state-assisted home-ownership schemes and a buoyant economy. By contrast, those entering in the late 1990s have experienced a much less favourable policy and economic environment. The paper also explores the extent to which price trajectories have varied in different sectors.

Calculating the price trajectory of adoption of fuel cell vehicles

How do you model consumer behaviour for disruptive technologies? Technologies that potentially have no antecedents and that, by their very definition, change consumer behaviour patterns? This paper outlines a methodology and results employed during a study to model the consumer willingness to pay for fuel cell vehicles, a potential disruptive innovation (DI). The first part of the study provides a short overview on DI highlighting why the fuel cell family of technologies may represent an upcoming DI. From the post ante study of successful historical disruptive innovations a number of initial `rules of adoption' can be sketched. Further narrowing of the focus on economic reasons for adoption provides a framework for which the willingness to pay for the new disruptive technology, such as, here, fuel cell vehicles, can be analysed during different phases of the market. This economic framework is then applied to the potential future market of fuel cell vehicles using information from a model that was built from vehicles during the build years 1994–2002 in the subcompact, compact and luxury class. The results presented in this paper concentrate on the subcompact and compact class of vehicle and supersede the initial results previously published. Finally, there is a short discussion on different pathways that this can be taken forward and used to help in policy decisions.

Computing price trajectories in combinatorial auctions with proxy bidding

Proxy bidding has proven useful in a variety of real auction formats – most notably eBay – and has been proposed for the nascent field of combinatorial auctions. Previous work on proxy bidding in combinatorial auctions requires the auctioneer to run the auction with myopic bidders to determine the outcome. In this paper, we present a radically different approach that computes the bidders’ allocation of their attention across the bundles only at “inflection points”. Inflections are caused by the introduction of a new bundle into an agent’s demand set, a change in the set of currently competitive allocations, or the withdrawal of an agent from the set of active bidders. This approach has several advantages over alternatives, including that it computes exact solutions and is invariant to the magnitude of the bids.

Bubble, Critical Zone and the Crash of Royal Ahold

Our analysis of financial data, in terms of super-exponential growth, suggests that the seed of the 2002/03 crisis of the Dutch supermarket giant AHOLD was planted in 1996. It became quite visible in 1999 when the post-bubble destabilization regime was well-developed and acted as the precursor of an inevitable collapse fueled by raising expectations of investors to maintain strong herding pressures. We have adapted Weidlich's theory of opinion formation to describe the formation of buy or sell decisions among investors, based on a competition between the mechanisms of herding and of personal opinion opposing the herd. Among four typical patterns of stock price evolution, we have identified a in the model characterized by a strong sensitivity of the price trajectory on the herding and personal inclination parameters. The critical zone describes the maturation of a systemic instability forewarning of an inevitable crash. Classification and recognition of the spontaneous emergence of patterns of stock market evolution based on Weidlich's theory of complex systems, and in particular our discovery of the post-bubble destabilization regime which acts as a precursor to a subsequent crash or antibubble, not only presents the possibility of developing early warning signals but also suggests to top management ways of dealing with the coming crisis.

Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000

Following our investigation of the USA Standard and Poor index anti-bubble that started in August 2000 (Quant. Finance 2 (2002) 468), we analyze 38 world stock market indices and identify 21 “bearish anti-bubbles” and six “bullish anti-bubbles”. An “anti-bubble” is defined as a self-reinforcing price trajectory with self-similar expanding log-periodic oscillations. Mathematically, a bearish anti-bubble is characterize by a power law decrease of the price (or of the logarithm of the price) as a function of time and by expanding log-periodic oscillations. We propose that bearish anti-bubbles are created by positive price-to-price feedbacks feeding overall pessimism and negative market sentiment further strengthened by inter-personal interactions. Bullish anti-bubbles are here identified for the first time. The most striking discovery is that the majority of European and Western stock market indices as well as other stock indices exhibit practically the same log-periodic power law anti-bubble structure as found for the USA S&P500 index. These anti-bubbles are found to start approximately at the same time, August 2000, in all these markets. This shows a remarkable degree of worldwide synchronization. The descent of the worldwide stock markets since 2000 is thus an international event, suggesting the strengthening of globalization.

NONPARAMETRIC ANALYSES OF LOG-PERIODIC PRECURSORS TO FINANCIAL CRASHES

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called (H, q)-analysis. The analysis using the (H, q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln (tc-t) variable, where tcis the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.