Price Path Research Articles

Price-Path Convexity, Extrapolation, and Short-Horizon Return Predictability

The curvature of intramonth stock price paths, which is distinct from cumulative return over the same period, contains significant additional return predictive power. In the cross section, stocks with the least convex price paths subsequently outperform stocks with the most convex price paths. This effect ranges from 1.34% to 1.53% per month and is not driven by small stocks, the bid-ask bounce, or other short-term return predictors. We find similar results in different time periods, in non-US G7 countries, and even at the aggregate market level. We argue that price-path convexity uniquely captures investor over-extrapolation of recent price changes. Therefore, our results provide broad evidence that extrapolative expectations are an important contributor to short-horizon return predictability.

Data-Driven Collusion and Competition in a Pricing Duopoly With Multinomial Logit Demand

We consider dynamic pricing and demand learning in a duopoly, both from the perspective where the firms compete against each other and from the perspective where the firms aim to collude to increase their revenues. We adopt the widely studied multinomial logit demand model and construct a sustainable notion of collusion, called fair Pareto optimal pricing, that ensures equal relative revenue improvements for both firms compared to the Nash equilibrium. In contrast to other notions of collusion such as joint-revenue maximization, we show that fair Pareto optimal pricing is always detrimental for consumers and profitable for both firms in the duopoly, regardless of the model parameters. Next, we construct a price algorithm that learns the fair Pareto optimal price from accumulating data if deployed by both firms in the duopoly, and prove theoretical performance bounds. In addition, we propose a mechanism to infer demand observations from the competitor's price path, so that our algorithm can operate in a setting where prices are public but demand is private information. We also construct a price algorithm for the case that the firms compete against each other, and show that it learns to respond optimally against a class of algorithms that includes best-response and fixed-price policies. Our work contributes to the understanding of well-performing price policies in a competitive multi-agent setting, and also shows that collusion by algorithms is in theory possible and deserves the attention of lawmakers and competition policy regulators.

Option pricing for rice by using Feynman path integral

The options are contracts that give a holder the right to buy or sell an underlying asset at the specific price before or on the expiration date. In return, the holder must pay the premium, the price of an option, to the seller in order to make contracts. As the financial problem occurs with many Thai farmers because of the fluctuation of agricultural product price. In this work, we try to price the American put option by using Feynman path integral in order to create the rice price insurance. The numerical procedures are separated into 2 parts. Firstly, the Atlantic path is determined by quasi-European method. Secondly, hybrid lattice Monte-Carlo method is used to simulate the underlying asset price path in order to evaluate the expectation profit of the option, or the premium. Moreover, the volatility rate of rice price is determined. As a result, the premium of American put option for rice is determined, and there is a deviation less than 8% comparing with Monte Carlo valuation with LSM algorithm in these examples. However, the result suggests that in this work’s assumption, the option pricing by using Feynman path integral is not effective to be used.

The Visual Shape Score: On its Predictability in the Lab, the Aggregated Stock Market, and the Cross-Section of Stock Returns

We introduce a simple and highly portable measure capturing the impact of price path visualizations on investor behavior, beliefs, and financial market outcomes: the visual shape score (VSS). The score reflects the degree of convexity of a price path. Although VSS is only a single metric, it captures four aspects of price path visualizations: bottom-up visual salience, top-down effects like evoked emotions, visual pattern recognition, and simplifications due to visualisation. Experimental findings suggest that more convex shapes positively explain investors' return expectations, their stated stock attractiveness, and investments. We augment the experimental results with field data. We find that VSS can help to better understand beliefs elicited from survey data and that VSS exhibits return predictability among individual stocks beyond a large range of cross-sectional return predictors.

Hedging and temporal permit issuances in cap-and-trade programs: The Market Stability Reserve under risk aversion

Cap-and-trade programs such as the European Union's Emissions Trading System (EU ETS) expose firms to considerable risks, to which the firms can respond with hedging. We develop an intertemporal stochastic equilibrium model to analyze the implications of hedging by risk-averse firms. We show that the resulting time-varying risk premium depends on the size of the permit bank. Applying the model to the EU ETS, we find that hedging can lead to a U-shaped price path, because prices initially fall due to negative risk premiums and then rise as the hedging demand declines. The Market Stability Reserve (MSR) reduces the permit bank and thus, increases the hedging value of the permits. This offers an explanation for the recent price hike, but also implies that prices may decline in the future due to more negative risk premiums. In addition, we find higher permit cancellations through the MSR than previous analyses, which do not account for hedging.

Hedging and the Temporal Permit Issuance in Cap-and-Trade Programs: The Market Stability Reserve Under Risk Aversion

Cap-and-trade programs such as the European Union’s Emissions Trading System (EU ETS) expose firms to considerable risks, to which the firms can respond with hedging. We develop an intertemporal stochastic equilibrium model to analyze the implications of hedging by risk-averse firms. We show that the resulting time-varying risk premium depends on the size of the permit bank. Applying the model to the EU ETS, we find that hedging can lead to a U-shaped price path, because prices initially fall due to negative risk premiums and then rise as the hedging demand declines. The Market Stability Reserve (MSR) reduces the permit bank and thus, increases the hedging value of the permits. This offers an explanation for the recent price hike, but also implies that prices may decline in the future due to more negative risk premiums. In addition, we find higher permit cancellations through the MSR than previous analyses, which do not account for hedging.

The drift burst hypothesis

The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms of liquidity provision. We show how to build drift bursts into the continuous-time Itô semimartingale model, elaborate on the conditions required for the process to remain arbitrage-free, and propose a nonparametric test statistic that identifies drift bursts from noisy high-frequency data. We apply the test and demonstrate that drift bursts are a stylized fact of the price dynamics across equities, fixed income, currencies and commodities. Drift bursts occur once a week on average, and the majority of them are accompanied by subsequent price reversion and can thus be regarded as “flash crashes.” The reversal is found to be stronger for negative drift bursts with large trading volume, which is consistent with endogenous demand for immediacy during market crashes.

Managing combined power and heat portfolios in sequential spot power markets under uncertainty

The integrated provision of energy among various energy sectors plays an important role in the process of decarbonisation of large energy systems. An important pillar is thereby the decarbonisation of the heat sector, where nowadays still a large percentage of heat supply originates from high-emission fossil fuels like coal or oil. In Central Europe, combined heat and power (CHP) plant applications, e.g. in local district heating networks, represent established methods to provide both electricity and heat at the same time, lowering overall fuel demands and lowering concomitant emissions. Heat pumps, converting electricity into heat, are also increasingly adopted by commercial (and household) customers. However, the optimal marketing and production scheduling of the heat and power- providing portfolios under price uncertainty is a challenging and often complex task. The importance of proper uncertainty handling is underscored even more if the optimal dispatch of flexible technologies like storages needs to be considered. In this paper, we propose an enhanced multi-stage stochastic programming model for coordinated bidding in two sequential markets, namely the one-hour and the fifteen-minute electricity products in the German (day-ahead) spot market. Our study develops and applies a stochastic mixed-integer linear programming model for a virtual power plant, acting as a price taker in the mentioned electricity markets. The model determines the optimal bidding strategies for a heterogeneous portfolio of small gas-fired motor- CHP units, heat pumps, electric storage heaters and battery storage systems. Thereby, we introduce a novel approach to construct piece-wise linear bidding curves for these markets, choosing their supporting points based on the simulated price paths. For the evaluation of the benefits of decision-making by help of stochastic modelling and optimization with different scenario numbers, we develop a new concept, the Benefit of Stochastic Optimization (BSO) and reflect and contrast our results with the computational burden of stochastic simulation, using the example of a real-world portfolio. We find that stochastic optimisation is a valuable optimisation method that may inform and improve individual marketer’s decision-making processes. However, the observable additional benefits, i.e. compared to deterministic point forecasts, are limited in the investigated cases, while computational expensiveness increases significantly when adding further scenarios.

How uncertainty in technology costs and carbon dioxide removal availability affect climate mitigation pathways

Limiting global warming to “well below 2°C” as stated in the Paris Agreement requires ambitious emissions reductions from all sectors. Rapid technology cost declines in the energy sector are changing energy investment and emissions, even with the weak climate policies currently in place. We assess how energy supply costs and carbon dioxide removal (CDR) availability affect mitigation by performing a sensitivity analysis with the energy-economy-climate model REMIND. We use new scenarios with carbon price paths that aim to reduce the frequently seen temperature overshoot. Further, we measure the sensitivities of mitigation indicators to the costs of technologies across economic sectors. We assess the sensitivity to nine techno-economic parameters: the costs of wind, solar, biomass, gas, coal, oil, nuclear, and electric/hydrogen vehicles, as well as the injection rate of Carbon Capture and Storage (CCS). While technology costs play a role in shaping optimal pathways, we find that transport sector costs affect the economics of deep decarbonization, whereas costs of renewables are more important for scenarios under weak climate policies. This further highlights the value of renewable energy deployment as a no-regrets option in climate policy. In terms of the sensitivity of model outputs, economic indicators become more sensitive to costs than emissions, with increasing policy stringency.

Stress testing household debt

We estimate a county-level model of household delinquency and use it to conduct of household debt. Applying house price and unemployment rate shocks from Comprehensive Capital Analysis Review (CCAR) stress tests, we find that forecasted delinquency rates for the recent stock of debt are moderately lower than for the stock of debt before the 2007-09 financial crisis, given the same set of shocks. This decline in expected delinquency rates under stress reflects an improvement in debt-to-income ratios and an increase in the share of debt held by borrowers with relatively high credit scores. Under an alternative scenario where the size of house price shocks depends on housing valuations, we forecast a much lower delinquency rate than occurred during the crisis, reflecting more reasonable housing valuations than pre-crisis. Stress tests using other scenarios for the path of house prices and unemployment also support the conclusion that household debt curren tly poses a lower risk to financial stability than before the financial crisis.

Geometric fractional Brownian motion model for commodity market simulation

The geometric Brownian motion (GBM) model is a mathematical model that has been used to model asset price paths. By incorporating Hurst parameter to GBM to characterize long-memory phenomenon, the geometric fractional Brownian motion (GFBM) model was introduced, which allows its disjoint increments to be correlated. This paper investigates the accuracy of GBM and GFBM in modelling Malaysia’s crude palm oil price simulation, and to see display of persistent or anti-persistent behaviour across different periods. Results show that the GFBM model is more accurate than the GBM model in simulating future price path for the given data set.

Carbon Pricing and the Elasticity of CO2 Emissions

We study the impact of carbon pricing on CO2 emissions across five sectors for a panel of 39 countries over 1990-2016. Using newly constructed sector-level carbon price data, we implement a novel approach to estimate the changes in CO2 emissions associated with (i) the introduction of carbon pricing regardless of the price level; (ii) the implementation effect as a function of the price level; and (iii) post-implementation marginal changes in the CO2 price. We find that the introduction of carbon pricing has reduced growth in CO2 emissions by 1% to 2.5% on average relative to counterfactual emissions, with most abatement occurring in the electricity and heat sector. Exploiting variation in carbon pricing to explain heterogeneity in treatment effects, we find an imprecisely estimated semi-elasticity of a 0.05% reduction in emissions growth per average $1/metric ton (hereafter abbreviated as: ton) of CO2. After the carbon price has been implemented, each marginal price increase of $1/tCO2 has temporarily lowered the growth rate of CO2 emissions by around 0.01%. These are disappointingly small effects. Simulating potential future emissions reductions in response to carbon price paths, we conclude that – in the absence of complementary non-pricing policy interventions – carbon pricing alone, even if implemented globally, is unlikely to be sufficient to achieve emission reductions consistent with the Paris climate agreement.

Approximate Analytical Pricing of European Options under the Non-affine Stochastic Volatility Model

The non-affine stochastic volatility model has attracted increasing attention in recent years, due to its excellent performance in describing the nonlinear characteristics of asset price path. However, the fact that there is no close-form of option pricing formula under this model, restricts its use badly. To remove this restriction, two approximate analytical option pricing approaches are proposed in this paper, that is, the piecewise first-order Taylor expansion method and the perturbation-based asymptotic expansion method of implied volatility. The first method is used to derive an approximate characteristic function, then based on which the Fourier-Cosine expansion method calculates the European option price. In the second way, implied volatility of the European option price is asymptotically expanded around non-affine term of volatility. Compared with the existing methods in literature, numerical experiments show that the first method has higher accuracy, while the second method is of more practical significance. In addition, the accuracy of the first method is generally higher than that of the second method in most cases, while the second method performs better when the volatility is extremely small.

Capital Gains Overhang with a Dynamic Reference Point

Financial models incorporating a reference point, such as the Capital Gains Overhang (CGO) model, typically assume it is fixed at the purchase price. Combining experimental and market data, this paper examines whether such models can be improved by incorporating reference-point adjustment. Using real stock prices over horizons from 6 months to 5 years, experimental evidence demonstrates that a number of salient points in the prior share price path are key determinants of the reference point, in addition to the purchase price. Market data testing is then undertaken by using the CGO model. We show that composite CGO variables, created by using a mix of salient points with weights determined in the experiment, have greater predictive power than the traditional CGO variable in both cross-sectional U.S. equity-return analysis and when analyzing the performance of double-sorted portfolios. In addition, future trading volume is more sensitive to changes in the composite CGO variables than to the traditional CGO, further emphasizing the importance of adjusting reference points. This paper was accepted by Tyler Shumway, Finance.

Mechanics of good trade execution in the framework of linear temporary market impact

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably, however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler–Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.

The potential impact of Covid-19 on the Irish housing sector

PurposeThis paper aims to examine the implications for the Irish housing market of the economic slowdown due to the Covid-19 virus.Design/methodology/approachIn this paper, an inverted demand function for housing is augmented to include a residential market activity variable and estimate the impact on house prices of the decline in economic activity due to the virus-related measures. The likely future path of house prices based on two different recovery scenarios is also examined. Under both scenarios house prices are forecast to decline in the near term.FindingsThe scenario analysis presented here indicates that Irish house prices are set to fall over the next 18 months as a result of the Covid-19 downturn. This contraction in prices is due to the decline in household disposable income and the sharp fall-off in mortgage market activity, which will inevitably result from the administrative closedown implemented by the Irish authorities.Originality/valueAs such the approach builds on several studies which have examined both house price movements in general and the relationship between house prices and mortgage credit availability. The paper also draws on the latest analysis of the implications for the Irish economy of Covid-19 and the related administrative closure methods introduced by the public authorities.

The role of sentiment in housing market with credit-led funding: the case of Turkey

This paper investigates the long run relationship among sentiment, which is defined as the aggregate investor attitude, housing credit and prices, and supply in Turkish housing market over the period of 2010:01 and 2018:06. The empirical results indicate that there is a long run relation among above stated variables. This study confirms the role of credit in explaining the increases in house prices. Importantly, this paper finds that the sentiment is significant in forecasting housing credit volume and supply on housing in the short run. The results also highlight the importance of sentiment as a factor at work in explaining the housing prices and supply of dwellings in the long run. Moreover, counterfactual scenarios on house price path suggests that the housing prices are sensitive to changes in sentiment as in credit volume, but with a lesser magnitude.

Informational Robustness in Intertemporal Pricing

Abstract We introduce a robust approach to study dynamic monopoly pricing of a durable good in the face of buyer learning. A buyer receives information about her willingness-to-pay for the seller’s product over time, and decides when to make a one-time purchase. The seller does not know how the buyer learns but commits to a pricing strategy to maximize profits against the worst-case information arrival process. We show that a constant price path delivers the robustly optimal profit, with profit and price both lower than under known values. Thus, under the robust objective, intertemporal incentives do not arise at the optimum, despite the possibility for information arrival to influence the timing of purchases. We delineate whether constant prices remain optimal (or not) when the seller seeks robustness against a subset of information arrival processes. As part of the analysis, we develop new techniques to study dynamic Bayesian persuasion.

Empirical analysis of how political ideology and ownership influence price stability in the Swedish district heating market

It is known that regulators and customers value stable prices in monopolised energy markets. The purpose of this paper is to investigate what factors influence local energy distributors to care about, and seek to implement, stable prices. Because the literature has suggested that ownership and political ideology affect monopoly pricing behaviour, we pay particular attention to ideological and ownership heterogeneity across a large number of local jurisdictions in Sweden. Specifically, this paper investigates two different pricing aspects; first, actual pricing behaviour in the unregulated Swedish district heating market and, second, survey data where the district heating firms report how important they think price stability is for their level of competitiveness. The results show that district heating firms that operate in municipalities with a left-wing government (i) implement actual prices that follow the long-term price path to a larger extent and (ii) state that smoothed prices are more important for their level of competitiveness. Results are both statistically and economically significant at conventional levels.

A new unbiased additive robust volatility estimation using extreme values of asset prices

We propose a new unbiased robust volatility estimator based on extreme values of asset prices. We show that the proposed Add Extreme Value Robust Volatility Estimator (AEVRVE) is unbiased and is 2–3 times more efficient relative to the Classical Robust Volatility Estimator (CRVE). We put forth a novel procedure to remove the downward bias present in the data even without increasing the number of steps in the stock price path. We perform Monte Carlo simulation experiments to show the properties of unbiasedness and efficiency. The proposed estimator remains exactly unbiased relative to the standard robust volatility estimator in the empirical data based on global stock indices namely CAC 40, DOW, IBOVESPA, NIKKEI, S&P 500 and SET 50.