A dynamic analysis of moving average rules

The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper, we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the MA rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.     

A scenario-based integrated approach for modeling carbon price risk

Carbon prices are highly dependent on government emission policies and local industrial compositions. When historical data does not exist or limited price data can only be sourced from another country, scenario analysis becomes the only tool for the modelling of future carbon prices. However, various plausible but equally possible scenarios can produce large variations in forecast carbon prices. In a traditional approach of scenario analysis, investment decisions or risk management strategies are proposed and analysed for each given scenario, optimal solutions are determined. However, when the number of scenarios becomes large, it often becomes too complex and intractable to have a clear view on the selection of investment decisions or risk-management strategies because these decisions and strategies are closely linked with each of the many scenarios. In this paper, it is proposed to use a stochastic mean-reversion model to represent future carbon price movements, but this model is calibrated to the forecast carbon prices of all the scenarios. In this approach, a single model is used to capture the underlying uncertainty and expectation of the stochastic carbon prices as projected by all the scenarios, carbon price risk can thus be modeled and analysed without the need for direct references to any specific scenarios. The modelling and management of long-term carbon-price risk are therefore purely dependent on future carbon price levels and volatilities of these scenarios, instead of on the scenarios themselves. Through such an approach, the optimization of investment decisions and risk management solutions can be much simpler because the forecasted carbon prices are the only input data.      

Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions.     

Fundamentalists vs. chartists: Learning and predictor choice dynamics

In a simple, forward looking univariate model of price determination we investigate the evolution of expectations dynamics in the presence of two types of agents: fundamentalists and chartists. In particular, we combine evolutionary selection among heterogeneous classes of models through predictor choice dynamics based on a logit model, with adaptive learning in the form of parameters updating within each class of rules. We find that, for different parameterizations, it can happen that fundamentalists drive chartists completely out of the market or vice versa, and also that heterogeneous equilibria in which fundamentalists and chartists coexist are possible. Interestingly, though, only equilibria in which fundamentalists outperform chartists turn out to be adaptively learnable by agents.     

Why a simple herding model may generate the stylized facts of daily returns: explanation and estimation

The paper proposes an elementary agent-based asset pricing model that, invoking the two trader types of fundamentalists and chartists, comprises four features: (i) price determination by excess demand; (ii) a herding mechanism that gives rise to a macroscopic adjustment equation for the market fractions of the two groups; (iii) a rush towards fundamentalism when the price misalignment becomes too large; and (iv) a stronger noise component in the demand per chartist trader than in the demand per fundamentalist trader, which implies a structural stochastic volatility in the returns. Combining analytical and numerical methods, the interaction between these elements is studied in the phase plane of the price and a majority index. In addition, the model is estimated by the method of simulated moments, where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. A (parametric) bootstrap procedure serves to set up an econometric test to evaluate the model’s goodness-of-fit, which proves to be highly satisfactory. The bootstrap also makes sure that the estimated structural parameters are well identified.     

Dissecting the myth of the house price in Chinese metropolises: allowing for behavioral heterogeneity among investors

This paper aims to demystify the housing boom in Chinese metropolises by allowing for behavioral heterogeneity among investors. We construct an agent-based model where investors are categorized into two groups: fundamentalists and chartists. In addition, the investment strategy switching is allowed between these two groups contingent on the historical performance. Using the data of five Chinese metropolises over the period 2008–2014, the results suggest that chartists dominate the housing market and make the house price maintain an upward trend, while fundamentalists play a stabilizing role. Specifically, fundamentalists can serve as a “price anchor” in the market, because the proportion of the fundamentalists is negatively associated with both the growth rate of the house price and the deviation relative to the fundamental value. Overall, the impact of the chartists on the house price is much greater than that of the fundamentalists, which contributes to the ever-increasing house price in Chinese metropolises.

     

A zero-inflated ordered probit model,with an application to modelling tobacco consumption

Data for discrete ordered dependent variables are often characterised by “excessive” zero observations which may relate to two distinct data generating processes. Traditional ordered probit models have limited capacity in explaining this preponderance of zero observations. We propose a zero-inflated ordered probit model using a double-hurdle combination of a split probit model and an ordered probit model. Monte Carlo results show favourable performance in finite samples. The model is applied to a consumer choice problem of tobacco consumption indicating that policy recommendations could be misleading if the splitting process is ignored.     

A heterogeneous agent model of asset price dynamics with two time delays

This study constructs a heterogeneous agents model of a financial market in a continuous-time framework. There are two types of agents, fundamentalists and chartists. The former follows the traditional efficiency market theory and has a linear demand function, whereas the latter experiences delays in the formation of price trends and possesses a S-shaped demand function. The main feature of this study is a theoretical investigation on the effects caused by two time delays in a price adjustment process. In particular, two main results are demonstrated: One is that the stability switching curves are analytically derived, and the other is that the stability losses and gains can repeatedly occur when the shape of the curves are meandering. Although it is well known that a time delay has a destabilizing effect, these results imply that multiple delays can stabilize and destabilize a market price generating persistent deviations from the stationary price.     

Minimum return guarantees with fund switching rights—An optimal stopping problem

Recently, there is a growing trend to offer guaranteed products where the investor is allowed to shift her account/investment value between multiple funds. The switching right is granted a finite number of times per year, i.e. it is American style with multiple exercise possibilities. In consequence, the pricing and the risk management is based on the switching strategy which maximizes the value of the guarantee put-option. We analyze the optimal stopping problem in the case of one switching right within different model classes and compare the exact price with the lower price bound implied by the optimal deterministic switching time. We show that, within the class of log-price processes with independent increments, the stopping problem is solved by a deterministic stopping time if (and only if) the price process is in addition continuous. Thus, in a sense, the Black and Scholes model is the only (meaningful) pricing model where the lower price bound gives the exact price. It turns out that even moderate deviations from the Black and Scholes model assumptions give a lower price bound which is really below the exact price. This is illustrated by means of a stylized stochastic volatility model setup.     

Data envelopment analysis with stochastic variations in data

The mathematical programming-based technique data envelopment analysis (DEA) has often treated data as being deterministic. In response to the criticism that in most applications there is error and random noise in the data, a number of mathematically elegant solutions to incorporating stochastic variations in data have been proposed. In this paper, we propose a chance-constrained formulation of DEA that allows random variations in the data. We study properties of the ensuing efficiency measure using a small sample in which multiple inputs and a single output are correlated, and are the result of a stochastic process. We replicate the analysis using Monte Carlo simulations and conclude that using simulations provides a more flexible and computationally less cumbersome approach to studying the effects of noise in the data. We suggest that, in keeping with the tradition of DEA, the simulation approach allows users to explicitly consider different data generating processes and allows for greater flexibility in implementing DEA under stochastic variations in data.     

A Unified View of Signal Extraction, Benchmarking, Interpolation and Extrapolation of Time Series

Time series data are often subject to statistical adjustments needed to increase accuracy, replace missing values and/or facilitate data analysis. The most common adjustments made to original observations are signal extraction (e.g. smoothing), benchmarking, interpolation and extrapolation. In this article, we present a general dynamic stochastic regression model, from which most of these adjustments can be performed, and prove that the resulting generalized least square estimator is minimum variance linear unbiased. We extend current methods to include those cases where the signal follows a mixed model (deterministic and stochastic components) and the errors are autocorrelated and heteroscedastic.     

Heterogeneous expectations in the gold market: Specification and estimation

The increase in the price of gold between 2002 and 2011 appears to be a candidate for a potential asset price ‘bubble’, suggesting that chartists (feedback traders) were highly active in the gold market during this period. Hence, this paper develops and tests empirically several models incorporating heterogeneous expectations of agents, specifically fundamentalists and chartists, for the gold market. The empirical results show that both agent types are important in explaining historical gold prices but that the 10-year bull run of gold in the early 2000s is consistent with the presence of agents extrapolating long-term trends. Technically this paper is a further step toward providing an empirical foundation for certain assumptions used in the heterogeneous agents literature. For example, the empirical results presented in this paper compare the economical and statistical significance of numerous switching variable specifications that are generally only introduced ad hoc.     

Specification and estimation of dynamic demand systems incorporating polynomial price response functions: An application to U.S. clothing imports

Numerous recent empirical demand studies utilize the habit formation and state variable approaches to describe dynamic demand behavior. In this paper, we suggest the introduction of polynomial price response functions as an alternative method of generating dynamic conditional demand systems. This approach allows direct estimation of the degree of price substitutability among products and the timing of price effects. The application presented here involves the estimation of dynamic CES and indirect additive translog demand systems for U.S. clothing imports. The estimated price response lag structures and matrices of long-run price elasticities are presented and analyzed. Also, the precision of the non-parametric price elasticity estimates is evaluated by computing approximate asymptotic standard errors.     

Optimal fiscal and monetary policy with occasionally binding zero bound constraints

This paper studies optimal fiscal and monetary policy when the nominal interest rate is subject to the zero lower bound (ZLB) constraint in a stochastic New Keynesian economy. In the baseline model calibrated to match key features of the U.S. economy, it is optimal for the government to increase its spending when at the ZLB in the stochastic environment by about 60 percent more than it would in the deterministic environment. The presence of uncertainty creates a unique time-consistency problem if the steady state is inefficient. Although access to government spending policy increases welfare in the face of a large deflationary shock, it decreases welfare during normal times as the government reduces the nominal interest rate less aggressively before reaching the ZLB.     

Asset price volatility and banks

This paper examines the operation of Diamond–Dybvig banks when depositors have access to the asset market. Previous studies have shown that banks are redundant in this environment since it is impossible to prevent the strategic withdrawals. This paper shows that the strategic withdrawals can be prevented if the market risk, due to asset price volatility, is considered. Banks provide deterministic returns to the depositors since the aggregate withdrawals are predictable, and therefore, banks can choose the portfolio such that no asset liquidation is involved. However, an individual consumer with stochastic liquidity need is vulnerable to the price volatility if he holds the asset directly. Therefore, banks improve the consumers’ welfare by providing the insurance against not only the liquidity shock but also the market risk. Banks are not redundant.     

Technical inefficiency and productive decline in the U.S. interstate natural gas pipeline industry under the Natural Gas Policy Act

Firm-specific and temporal patterns of technical efficiency of the interstate natural gas transmission industry during the implementation of the Natural Gas Policy Act are estimated by two alternative methodologies. A new panel stochastic frontier systems estimator exploits the potential exogeneity of certain regressors from firm effects. This allows for heterogeneity in slopes, as well as in intercepts. Patterns of technical efficiency based on the structural stochastic model are compared with those based on deterministic programming methods, data envelopment analysis. Concordant findings based on these alternative methodologies suggest a perversive pattern of declining technical efficiency in the industry during the period of phased in well-head price deregulation.     

Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends

We investigate dynamical properties of a heterogeneous agent model with random dividends and further study the relationship between dynamical properties of the random model and those of the corresponding deterministic skeleton, which is obtained by setting the random dividends as their constant mean value. Based on our recent mathematical results, we prove the existence and stability of random fixed points as the perturbation intensity of random dividends is sufficiently small. Furthermore, we prove that the random fixed points converge almost surely to the corresponding fixed points of the deterministic skeleton as the perturbation intensity tends to zero. Moreover, simulations suggest similar behaviors in the case of more complicated attractors. Therefore, the corresponding deterministic skeleton is a good approximation of the random model with sufficiently small random perturbations of dividends. Given that dividends in real markets are generally very low, it is reasonable and significant to some extent to study the effects of heterogeneous agents’ behaviors on price fluctuations by the corresponding deterministic skeleton of the random model.     

Stochastic models of resonating markets

This paper describes a way to model a seasonally and irregularly peaking price dynamics, as that originated in commodity and energy markets, using a system of coupled nonlinear stochastic differential equations. The specific case of an electric power market is used to show which microeconomic features this approach is able to model. Critical point analysis is used in a simple way to show how the interaction between dynamic criticality and stochasticity can be used to develop further models, useful to explore more deeply other types of peaking price dynamics.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

The effect of systematic risk factors on counterparty default and credit risk of interest rate swaps

This research investigates the effect of specific systematic risk factors on credit risk pricing and capital allocation of interest rate swaps. Because of the stochastic nature of uncertain future cash flows and interest rates, practitioners typically employ the Black-Scholes option pricing model in combination with a simulation analysis to establish capital requirements and estimate the shadow price of an interest rate swap. However, this practice of pricing swap risk excludes systematic risk factors that affect the risk shadow price, thereby underestimating the capital allocation required for financial institutions. This research demonstrates the effect of risk mispricing when simulation models ignore systematic risk factors such as model risk, convexity risk, and parameter risk on the pricing of interest rate swaps.