Price Path Research Articles

Effects of price path shapes and decision frames on emotions and investment decisions: Experimental evidence

We extend the literature on emotions and financial decisions by varying the agent (private investor, fund manager, delegation to a fund manager) in an investment experiment. We additionally vary the decision situation (buy or sell) and the shape of displayed price paths (convex, concave, or straight). We measure the investment behavior and the emotional valence evoked by the price paths. Independent of the type of agent, we confirm that price path shapes are related to investment behavior and emotions. In particular, concave shapes are associated with lower investments and valence. Finally, we provide evidence for a mediating role of valence.

Higher order expectations, learning, and sentiment pricing dynamics

We present a dynamic asset pricing model combining individual investor sentiment, higher order expectations with learning. In the basic model, the forward-looking expectation of individual investors is distorted by individual sentiment and higher order expectations, so prices react more sluggishly to changes in fundamentals of the asset. We find that investor sentiment plays a significant role in the effect of higher order expectations on asset pricing. Investor sentiment not only makes the price tightly anchor to the initial price, but also increases the sentiment drift of the price. Higher order expectations exhibit inertia, therefore aggravating the anchor to the initial price. With the increase of the order, more and more investor sentiment is integrated into the prices, amplifying the bias of pubic signal relative to fundamentals. When individual sentiment investors learn valuable public information through price system in the long term, the information component of the equilibrium price increases, thus drawing the asset price back toward the rational expected value. The model could offer a partial explanation to the inertia and drift in the price path

Path shadowing Monte Carlo

We introduce a Path Shadowing Monte Carlo method, which provides the prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or ‘shadows’, the actual (observed) history. We test our approach using paths generated from a maximum entropy model of financial prices, based on a recently proposed multi-scale analogue of the standard skewness and kurtosis called ‘Scattering Spectra’. This model promotes the diversity of generated paths while reproducing main statistical properties of financial prices, including stylized facts such as volatility roughness. Our method yields state-of-the-art predictions for future realized volatility and allows one to determine conditional option smiles for the S&P500 that outperform both the most recent low-parametric models and the option market itself. The code is available at https://github.com/RudyMorel/shadowing (This work is supported by the PRAIRIE 3IA Institute of the French ANR-19-P3IA-0001 program and the ENS-CFM models and data science chair.).

Impact of different CO2 price paths on the development of the European electricity system

In energy system transformation studies, the assumption of linearly rising CO2 prices is common and based on the decreasing issued European allowances (EUA). The actual auction price for allowances is influenced by market dynamics, resulting in non-linear variations in CO2 prices due to the possibility of banking allowances. This study explores the impact of non-linear CO2 price trajectories on the European electricity market. Various scenarios, such as increasing prices with the market interest rate, early price peaks, collapse, or fluctuations, are examined until 2030. The study quantifies the effects on power plant investments, profitability, consumer costs, and government revenues. The findings reveal that early and high price signals lead to an earlier transition with 7 % more wind power plants but at 4 % higher costs. Conversely, lower initial prices delay power plant investments in wind power plants by 6 % and result in 21 % higher emissions. Compensation for climate impact costs can yield a positive cost-benefit analysis in scenarios with early and high price signals when emissions are avoided through mechanisms like the Market Stability Reserve (MSR).

My money—My problem: How fear‐of‐missing‐out appeals can hinder sustainable investment decisions

AbstractCryptocurrencies (cryptos) have detrimental environmental effects due to their massive energy consumption. While several green crypto coins have been launched, the mainstream—environmentally unfriendly coins—still lead the market. In this study, we explore if influencer marketing, specifically fear‐of‐missing‐out (FOMO) appeals, can contribute to promoting green crypto coin purchases to encourage sustainable investments. The results of five studies (two lab experiments using neurobiological sensors, two online experiments, and a discrete choice experiment) show that social media postings conveying FOMO appeals decrease (increase) green crypto (normal crypto) coin investments. The results further show that message congruence and emotional value perceptions mediate this effect. Finally, we demonstrate that the observed results hold when adding governance and regulatory crypto support as well as the crypto price path evolution to the choice. The results provide notable theoretical contributions and implications for policymakers concerned with fostering more sustainable consumption behavior in the crypto context.

Biochar as a carbon dioxide removal strategy in integrated long-run mitigation scenarios

Limiting global warming to under 2 °C would require stringent mitigation and likely additional carbon dioxide removal (CDR) to compensate for otherwise unabated emissions. Because of its technology readiness, relatively low cost, and potential co-benefits, the application of biochar to soils could be an effective CDR strategy. We use the Global Change Analysis Model, a global multisector model, to analyze biochar deployment in the context of energy system uses of biomass with CDR under different carbon price trajectories. We find that biochar can create an annual sink of up to 2.8 GtCO2 per year, reducing global mean temperature increases by an additional 0.5%–1.8% across scenarios by 2100 for a given carbon price path. In our scenarios, biochar’s deployment is dependent on potential crop yield gains and application rates, and the competition for resources with other CDR measures. We find that biochar can serve as a competitive CDR strategy, especially at lower carbon prices when bioenergy with carbon capture and storage is not yet economical.

Agent based modeling for intraday electricity markets

AbstractIn recent years, the strong growth of renewable energy sources has led to considerable instability in the electricity markets. As a consequence, this has increased trading activities in the continuous intraday market, especially close to delivery. This work presents an agent-based model that is able to reproduce the continuous market evolution, distinguishing players in dispatchable and non-dispatchable power plants and analyzing the behavior and interactions between them. All players behave rationally, trying to maximize their revenues and minimize imbalances. The results show that the model is able to reproduce the main characteristics of the continuous intraday electricity market, such as the price path strongly dependent on internal and external information, such as the wind production forecast, possible outages, an increase in order arrival towards the end of the trading session and weak market efficiency. The strategies assigned to each agent have been formulated taking into account statistical analyses of historical orders placed during continuous trading in different European bidding zones. The analyses have been carried out in a scenario composed of thermal plants with different marginal costs and wind agents, but the flexibility of the model gives the possibility to study many different scenarios.

Pendekatan Metode Monte Carlo untuk Simulasi Pergerakan Harga Saham

This research applies the Monte Carlo simulation method to predict the movement of Apple Inc.'s stock price over a long period of time. Using historical data of Apple's stock price from 12 December 1980 to 24 March 2022, this study aims to generate a probability distribution of the future stock price. The method involves several steps, including data collection, log return calculation, parameter estimation, and simulation of the stock price path through random iterations based on the log return distribution. The simulation results show that the closing price of Apple stock can be predicted by following the historical trend, although there are differences with the real data due to the stochastic nature of the Monte Carlo technique. This research also applies a variance reduction method to improve simulation efficiency. The findings provide a valuable perspective for investors and financial analysts in identifying investment risks and opportunities through an in-depth understanding of the dynamics of stock price movements using Monte Carlo simulation. Suggestions for future research include the use of VaR methods with historical variance and covariance approaches, as well as considering longer data periods and more stock indices for more comprehensive results.

Designing product upgrades in the presence of online consumer reviews

AbstractWhen consumers decide whether to buy an experience good, they usually search for online reviews to reduce quality uncertainty. In this paper, we consider that consumers may strategically wait for the new generation product and consult reviews of the previous generation product in the same series while facing sequential launching products. We develop a two‐period analytical model analyzing how the presence of intergenerational reviews influences the firm's decision on product upgrades. Our analysis obtains three main findings. First, when online reviews are less efficient and consumers are more strategic, the firm should skip the old product due to the severe product cannibalization effect. Second, negative reviews discourage the firm from quality improvement, and positive reviews drive the firm to provide quality improvement at a high price. Third, the firm chooses a decreasing price path without online reviews. However, an increasing price path is preferred in the presence of online reviews when online reviews are positive, the efficiency of consumer reviews is high, and consumers are more strategic. Our study indicates that online reviews have important influence on product generation design, and the firm should carefully evaluate online reviews of the old product when designing its new generation product.

Simulation-based Forecasting for Intraday Power Markets: Modelling Fundamental Drivers for Location, Shape and Scale of the Price Distribution

During the last years, European intraday power markets have gained importance for balancing forecast errors due to the rising volumes of intermittent renewable generation. However, compared to day-ahead markets, the drivers for the intraday price process are still sparsely researched. In this paper, we propose a modelling strategy for the location, shape and scale parameters of the return distribution in intraday markets, based on fundamental variables. We consider wind and solar forecasts and their intraday updates, outages, price information and a novel measure for the shape of the merit-order, derived from spot auction curves as explanatory variables. We validate our modelling by simulating price paths and compare the probabilistic forecasting performance of our model to benchmark models in a forecasting study for the German market. The approach yields significant improvements in the forecasting performance, especially in the tails of the distribution. At the same time, we are able to derive the contribution of the driving variables. We find that, apart from the first lag of the price changes, none of our fundamental variables have explanatory power for the expected value of the intraday returns. This implies weak-form market efficiency as renewable forecast changes and outage information seems to be priced in by the market. We find that the volatility is driven by the merit-order regime, the time to delivery and the closure of cross-border order books. The tail of the distribution is mainly influenced by past price differences and trading activity. Our approach is directly transferable to other continuous intraday markets in Europe.

Analisis Kebijakan Moneter melalui Jalur Harga Aset di Negara Muslim Berkembang

This research aims to analyze the contribution of variables from the interaction of monetary policy transmission variables (SBI, STOCK, INVESTMENT, GDP, INFLATION). This research uses secondary data or time series, namely from the first quarter of 2011 to the first quarter of 2016. The data analysis model in this research is Vector Autoregression (VAR) model and sharpened with Impulse Response Function (IRF) and Forecast Error Variance Decomposition (FEVD) analysis. The results of the VAR analysis show that the past variable (t-1) contributes to the current variable both the variable itself and other variables and from the estimation results it turns out that there is a reciprocal relationship between the variables where all the variables are monetary policy transmission variables (SBI, STOCK, INVESTMENT, GDP, INFLATION) contribute to each other. The results of the IRF analysis show that the stability of the response of all variables is formed in period 5 or the medium and long term, where the response of other variables to changes in one variable shows different variations from positive to negative responses or vice versa, and there are variables whose responses remain positive or remains negative from the short term to the long term. The results of the FEVD analysis show that there are variables that have the largest contribution to the variable itself in the short, medium and long term, such as GDP and SB. Meanwhile, other variables that have the greatest influence on the variable itself in the short, medium and long term are GDP which is most influenced by INVESTMENT, Inflation is most influenced by GDP, INVESTMENT is most influenced by Inflation, SB is most influenced by INVESTMENT while it is most influenced by SB. The results of the analysis of the interaction of each monetary policy transmission variable in the path of asset prices in developing Muslim countries in the short, medium and long term show that monetary policy transmission can increase economic growth and achieve the inflation targets of developing Muslim countries.

Bursting the bitcoin bubble: Do market prices reflect fundamental bitcoin value?

This paper develops a theoretical model of the bitcoin market and demonstrates that the bitcoin’s volatile and explosive price path is a consequence of the Bitcoin protocol’s system of supply management. The model implies that the marginal cost of mining the target supply of bitcoins is the fundamental value of the bitcoin since it corresponds to an equilibrium in the Bitcoin protocol and the rent-seeking tournament among miners. The data provide strong empirical evidence of cointegration between the bitcoin’s price and the marginal cost of mining the target supply of bitcoins, demonstrating the existence of their long-run equilibrium relationship. Current bubble detection techniques indicate that there is no evidence of explosive departures in the price of the bitcoin from its model-implied fundamental value. Since the raw price data exhibit explosive behavior, the apparent bubbles in the price of the bitcoin can be attributed to its nonstationary market fundamentals.

Dynamic pricing using flexible heterogeneous sales response models

We combine nonparametric price response modeling and dynamic pricing. In particular, we model sales response for fast-moving consumer goods sold by a physical retailer using a Bayesian semiparametric approach and incorporate the price of the previous period as well as further time-dependent covariates. All nonlinear effects including the one-period lagged price dynamics are modeled via P-splines, and embedding the semiparametric model into a Hierarchical Bayesian framework enables the estimation of nonlinear heterogeneous (i.e., store-specific) immediate and lagged price effects. The nonlinear heterogeneous model specification is used for price optimization and allows the derivation of optimal price paths of brands for individual stores of retailers. In an empirical study, we demonstrate that our proposed model can provide higher expected profits compared to competing benchmark models, while at the same time not seriously suffering from boundary problems for optimized prices and sales quantities. Optimal price policies for brands are determined by a discrete dynamic programming algorithm.

Pricing a resettable convertible bond based on decomposition method and PDE models

In this paper, a partial differential equation approach based on the underlying stock price path decomposition is developed to price an American-style resettable convertible bond. The American-style resettable convertible bond is viewed as a mixture of three simple securities, which can be used to replicate the feature of payoffs of the resettable convertible bond completely. The partial differential equations under the Black–Scholes framework are established to price these simple securities. An implicit Euler method is used to discretize the first-order time derivative while a central finite difference method on a piecewise uniform mesh is used to discretize the spatial derivatives. The error estimates are developed by using the maximum principle in two mesh sets both for the time semi-discretization scheme and the spatial discretization scheme, respectively. It is proved that the scheme is first-order convergent for the time variable and second-order convergent for the spatial variable. Numerical experiments support these theoretical results.

A càdlàg rough path foundation for robust finance

Using rough path theory, we provide a pathwise foundation for stochastic Itô integration which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called property (RIE) for càdlàg paths, which is shown to imply the existence of a càdlàg rough path and of quadratic variation in the sense of Föllmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Cover’s universal portfolio are admissible integrands, and that property (RIE) is satisfied by both (Young) semimartingales and typical price paths.

An empirically sufficient form for Sraffa prices

This paper examines three propositions: Sraffa's comment that Marx was “of course” right in thinking that labor value and “Sraffa price” (prices expressed relative to Sraffa's standard commodity) aggregates are essentially the same: empirical deviations of various aggregate components of total output are around five percent. This should be reflected in small representative models. Second, Pasinetti is correct that actual Sraffa price paths are generally simpler than those in the theoretical literature – as confirmed by the 403 industry price curves of the US 2002 input-output matrix. Third, as has been often demonstrated, Marx's transformation procedure is an iterative procedure for deriving Sraffa prices. Bienenfeld derives powerful first and second iterates, each beginning and ending at the corresponding individual Sraffa price curves. The simple nonlinear form of the second iterate provides excellent fits for the 403 Sraffa price curves. It is therefore an empirically sufficient general form of such price curves.

Structural estimates of the South African sacrifice ratio

This paper estimates the output cost of fighting inflation—the sacrifice ratio—for the South African economy using quarterly data spanning the period 1998:1–2019:3. To compute the sacrifice ratio, the structural vector autoregressive (SVAR) model developed by Cecchetti and Rich (2001) based on Cecchetti (1994) is employed. Our findings show us a small sacrifice ratio, which lies within the range 0.00002–0.231 percent with an average of 0.031 percent, indicating a low level of output to be sacrificed while fighting inflation. Hence, the reserve bank is recommended to sustain an inflation rate within the target range and reap the benefits of a predictable and stable price path, as restrictive monetary policy has only a transitory effect on real variables like output.

Dynamic pricing and production control in a two‐item make‐to‐stock system with flexible dual sourcing and lost sales

We consider a joint control of pricing and production in a two‐item inventory system, where each item can be produced by its dedicated source or a shared flexible source, under the lost‐sales setting. The demands of the two items are correlated. Due to the complexity caused by the lost‐sales assumption and the interplay between pricing and production decisions, we show the optimal value function satisfies five structural properties under certain conditions. The optimal ordering and pricing policies are then fully characterized by five production curves and two pricing functions. Different from existing literature, we show that the optimal price path may not be monotone in the inventory level of either item. Next, we estimate the value of flexibility by comparing two systems, one with the flexible source only and the other with the dedicated source only, and show that the value of flexibility is positive (or negative) if the flexible source has a faster (or slower) production rate and a lower (or higher) production cost. Through numerical experiments, we find that in most cases flexibility and dynamic pricing are substitutes except for a few exceptions; and product substitution can either increase or decrease the value of flexibility.

Dynamic pricing in the presence of social externalities and reference-price effect

This paper considers the pricing of a new product in the face of sophisticated consumer behaviors. At the individual level, consumers are forward-looking, whereby they may wait strategically for better purchasing opportunities. Additionally, and in line with prospect theory, consumers might also look back to form a reference-price point with which they can compare the current price. Consumers are assumed to be loss averse where losses resonate more than gains. Moreover, we account for the role of social influences in the form of externalities in consumers’ adoption decision. We develop progressively different nested models to examine the impact of each behavior. Two types of pricing regimes, that is, preannounced and responsive pricing, are utilized where the firm commits to the price path from the outset in the former while it does not in the latter. We find that a penetration pricing strategy can be both strengthened or weakened by forward-looking consumer behavior depending on the underlying dynamics. Our results also suggest that the superiority of the firm’s profit under committed pricing depends heavily on the consumer behaviors.

Market Liquidity Estimation in a High-Frequency Setup

This article deals with the identification of a superior forecasting method for market liquidity using a calibrated Heston model for the bid/ask price path simulation instead of a standard Brownian motion, as well as a compound Poisson process and inverse transform sampling for the generation of the bid/ask volume distribution. We show that the simulated trading volumes converge to one single value, which can be used as a liquidity estimator, and find that the calibrated Heston model as well as the inverse transform sampling are superior to both the use of standard Brownian motion and compound Poisson process.