Linear Pricing Research Articles

Linear beta pricing with efficient/inefficient benchmarks and short-selling restrictions

We provide two security pricing models that can be used when short sales of risky securities are not permitted. The first model uses a benchmark located on the expected return-standard deviation efficient frontier without short sales and presents security expected returns as a weighted linear function of two betas, one induced by the benchmark and the other adjusting for the short-sale constraints. The second model uses a benchmark that is inefficient relative to the efficient frontier, does not allow short sales, and expresses security returns as a weighted linear function of three betas:one induced by the inefficient benchmark, and the other two adjusting simultaneously for the short-sales restrictions and the benchmark's inefficiency.These results complement the linear pricing models that link expected returns and betas by allowing, for efficient or inefficient expected return-standard deviation, benchmarks with restricted short sales.

Urban Household Energy Consumption Forecasting Based on Energy Price Impact Mechanism

The energy price influence system is one of the key mechanisms in the study of energy consumption. China’s household energy consumption has obvious regional differences, and rising income levels and urbanisation have changed the willingness and ability of households to make energy consumption choices. Based on the linear price effect of household energy consumption, this paper explores the scenario characteristics of energy prices affecting energy consumption, taking electricity and natural gas consumption as examples. Based on household energy consumption statistics from 2005 to 2018 in 36 major cities across China, the accuracy and change trends of household energy consumption forecasts are investigated through the decision tree-support vector machine (DT-SVR) non-linear forecasting technique. The study shows that the non-linear forecasting technique accurately portrays the predicted trends of changes in total urban household electricity and natural gas consumption. Within the less developed regions of economic development, income levels are still the main constraint on changes in urban household energy consumption, and the stimulating effect of income levels on household energy consumption has not been seen in the process of economic development in these less developed regions. Urbanisation as an important factor in examining household energy consumption, different development patterns and development processes will gradually be reflected in scenario aspects such as the choice of urban household energy consumption and changes in total consumption.

Optimal fund menus

AbstractWe study the optimal design of a menu of funds by a manager who is required to use linear pricing and does not observe the beliefs of investors regarding one of the risky assets. The optimal menu involves bundling of assets and can be constructed from the solution to a calculus of variations problem that optimizes over the indirect utility that each type receives. We provide a complete characterization of the optimal menu and show that the need to maintain incentive compatibility leads the manager to offer funds that are inefficiently tilted towards the asset that is not subject to the information friction.

Product (Un)bundling under Repeat Purchases

We study multi-product (un)bundling under customers’ repeat purchases. Departing from the bundling literature that focuses on customers’ one-time purchases, we consider customers who make repeat purchases: they not only decide whether to purchase a product or bundle, but also determine how to purchase the product or bundle in a repeated manner. We develop a multi-product model of customers’ repeat purchases, provide a microscopic characterization of each individual customer’s purchase and consumption decisions, and solve the firm’s pricing problems under two commonly used pricing schemes, namely, separate selling and bundling. Unlike the classic one-off selling models which prove the superiority of bundling over separate selling, we find that customers’ repeat purchases allow the reverse to be true under very general conditions, which is further strengthened by the existence of a marginal cost. We also identify the effect of correlated product valuations on the profitability of bundling, and demonstrate how this effect under repeat purchases differs from its counterpart under one-time purchases. We consider mixed bundling and nonlinear pricing, and articulate how these more sophisticated pricing schemes can be used to enhance revenue. We show that introducing nonlinear pricing can overturn the dominance of separate selling over bundling established under linear pricing. Our analysis provides novel insights into multi-product pricing under customers’ repeat purchases. Our results highlight the critical role of the customer purchasing model, one-time purchases versus repeat purchases, in driving monopoly firms’ strategic choice of product (un)bundling.

Quality forecasts: Predicting when and how much markets value higher‐protein wheat

AbstractWheat markets stand out among other major crop commodity markets because pricing at the first point of exchange—typically a grain handling facility—is differentiated on specific quality characteristics. Moreover, the premiums and discounts that elevators offer to obtain grain of specific quality can be significant. The relative importance of quality premiums and discounts to farm‐level production and marketing decisions demonstrate a need to quantitatively measure and explain factors that affect elevators' wheat‐quality pricing decisions. This study develops an informed expectation model of elevators' quality‐based pricing strategies and empirically estimates the model from a lengthy dataset of weekly price observations. I find empirical evidence that elevators use linear pricing schedules, but more aggressively discount wheat with protein levels lower than a baseline than reward higher‐protein wheat. The results also indicate that weather characteristics, futures contract price indicators, and USDA Crop Progress reports are contributors to predicting the new crop protein premiums and discounts, and that out‐of‐sample accuracy for predicting how grain elevators will value wheat protein ranges between 70% and 80%.

Autoregressive Neural Network EURO STOXX 50 Forecasting Model Based on Principal Component Stock Selection

Purpose: The given study looks into forecast accuracy of a traditional ARIMA model while comparing it to Autoregressive Neural Network (AR-NN) model for 984 trading days on EURO STOXX 50 Index.
 Methodology: A hybrid model is constructed by combining ARIMA model and feed-forward neural network model aiming to attain linear and non-linear price fluctuations. The study also incorporates the investigation of component stock prices of the index, that can be selected to improve the predictability of the hybrid model. 
 Findings:The reached ARIMA (1,1,3) model showed higher scores than AR-NN model however integrating selected exogenous stock prices from the index components gave much notable accuracy results. The selected exogenous stocks were extracted after conducting PCA and model scores were compared via MAPE and RMSE.
 Unique contribution to theory, practice and policy: The major contribution of this work is to provide the researcher and fnancial analyst a systematic approach for development of intelligent methodology to forecast stock market. This paper also presents the outlines of proposed work with the aim to enhance the performance of existing techniques. Therefore, Empirical analysis is employed along with a hybrid model based on a feed-forward Neural Network. Lesser error is attained on the test set of Index stock price by comparing the performance of ARIMA and AR-NN while forecasting. Hence, The components of extracted Index stock price like exogenous features are added to make an influence from the AR-NN model.

High-dimensional test for alpha in linear factor pricing models with sparse alternatives

We consider the problem of testing for the presence of alpha in Linear Factor Pricing Models. We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the alternative hypothesis is sparse, i.e. the alpha vector is sparse. As a general alternative, we suggest to combine the max-of-squares type test and a sum-of-squares type test, to benefit from the power advantages of both tests. We apply the two proposed tests to the monthly returns on securities in the Chinese and the U.S. stock markets, respectively under the Fama–French three-factor model, and confirm the usefulness of the proposed tests in detecting the presence of alpha.

DISCRETE-TIME OPTIMAL EXECUTION UNDER A GENERALIZED PRICE IMPACT MODEL WITH MARKOVIAN EXOGENOUS ORDERS

This paper examines a discrete-time optimal execution problem with generalized price impact. Our main objective is to investigate the effect of price impact caused by aggregate random trade orders posed by small traders on the optimal execution strategy when orders of the small traders have a Markovian dependence. Our problem is formulated as a Markov decision process with state variables which include the last small traders’ aggregate orders. Over a finite horizon, a large trader with Constant Absolute Risk Aversion (CARA) von Neumann–Morgenstern (vN-M) utility function maximizes the expected utility from the final wealth. By applying the backward induction method of dynamic programming, we characterize the optimal execution strategy and optimal value function and conclude that the optimal execution strategy is a time-dependent affine function of three state variables. Moreover, numerical analysis prevails that the optimal execution strategy admits a “statistical arbitrage” via a round-trip trading, although our model considers a linear permanent price impact. The result differs from the previous prevailing one that a linear permanent price impact model precludes any price manipulation or arbitrage. Thus, considering a price impact caused by small traders’ orders with a Markovian dependence is significant.

Optimal trade execution for Gaussian signals with power-law resilience

We characterize the optimal signal-adaptive liquidation strategy for an agent subject to power-law resilience and zero temporary price impact with a Gaussian signal, which can include e.g an OU process or fractional Brownian motion. We show that the optimal selling speed is a Gaussian Volterra process of the form on , where and satisfy a family of (linear) Fredholm integral equations of the first kind which can be solved in terms of fractional derivatives. The term is the (deterministic) solution for the no-signal case given in Gatheral et al. [Transient linear price impact and Fredholm integral equations. Math. Finance, 2012, 22, 445–474], and we give an explicit formula for for the case of a Riemann-Liouville price process as a canonical example of a rough signal. With non-zero linear temporary price impact, the integral equation for becomes a Fredholm equation of the second kind. These results build on the earlier work of Gatheral et al. [Transient linear price impact and Fredholm integral equations. Math. Finance, 2012, 22, 445–474] for the no-signal case, and complement the recent work of Neuman and Voß[Optimal signal-adaptive trading with temporary and transient price impact. Preprint, 2020]. Finally we show how to re-express the trading speed in terms of the price history using a new inversion formula for Gaussian Volterra processes of the form , and we calibrate the model to high frequency limit order book data for various NASDAQ stocks.

Liquidity fluctuations and the latent dynamics of price impact

Market liquidity is a latent and dynamic variable. We propose a dynamical linear price impact model at high frequency in which the price impact coefficient is a product of a daily, a diurnal, and an auto-regressive stochastic intraday component. We estimate the model using a Kalman filter on order book data for stocks traded on the NASDAQ in 2016. We show that our price changes estimates, conditional on order flow imbalance, on average of real price changes variance. Evidence is also provided on the fact that the conditioning on filtered information improves the estimate of the LOB liquidity with respect to the one obtained from a static estimation of the price impact. In addition, an out-of-sample analysis shows that our model provides a superior out-of-sample forecast of price impact with respect to historical estimates.

Long-run expectations of households

The rational expectations assumption, e.g. in life-cycle models and portfolio-choice models, prescribes that all actions are in line with a well-structured and unbiased system of expectations. In reality, justification and identification of expectations are nontrivial, and we lack empirical evidence especially for the long run. This paper starts to fill this gap and elicits short-run and long-run expectations of a sample of households that is designed to be representative of the universe of German households. We focus on expectations about three highly welfare-relevant markets: the stock market, the labor market, and the housing market. We show that linear extrapolations of short-run expectations can approximate long-run expectations in the labor market, but not in financial or housing markets. In the latter two markets, long-run expectations of households are severely below linear price growth and far below historical values. This extreme pessimism does not extend to the labor market, where expectations are fairly close to historical values. We also document substantial heterogeneity of expectations by socio-economic and personal characteristics, e.g., females are more pessimistic than males about outcomes in all markets.

The Cross Section of MBS Returns

ABSTRACTWe present a simple, linear asset pricing model of the cross section of Mortgage‐Backed Security (MBS) returns. MBS earn risk premia as compensation for their exposure to prepayment risk. We measure prepayment risk and estimate risk loadings using prepayment forecasts versus realizations. Estimated loadings on prepayment risk decrease monotonically in securities' coupons relative to the par coupon, consistent with the predicted effect of prepayment on bond value. Prepayment risk appears to be priced by specialized MBS investors. The price of prepayment risk changes sign over time with the sign of a representative MBS investor's exposure to prepayment shocks.

Semi-equilibrium Pricing: The CAPM Formula

We present a new type of pricing method, the semi-equilibrium pricing method, which solves the optimal portfolios of investors first. This stage is consistent with the equilibrium pricing method, but the second stage of the semi-equilibrium pricing method uses only a part of the market clearing conditions rather than the entirety. Based on this, we show that the pricing formula by capital asset pricing model (CAPM) is not an equilibrium pricing formula but a semi-equilibrium pricing formula: When the CAPM formula is valid, the market may not be cleared. Only when the total market value of risky securities is given can the CAPM formula completely determine the price vector of the risky securities. Additionally, we point out that the stochastic discount factor (SDF) pricing formula is the result of investors' portfolio optimization, and the market clearing conditions are not involved at all. The SDF pricing formula is presented in the form of a linear pricing function and can be used as a foundation template to establish pricing functions.

Resource Management and Pricing for Cloud Computing Based Mobile Blockchain With Pooling

In a public blockchain system applying Proof of Work (PoW), the participants need to compete with their computing resources for reward, which is challenging for resource-limited devices. Mobile blockchain is proposed to facilitate the application of blockchain for mobile service, in which the lightweight devices can participate mining by renting resources from the Cloud Computing Service Provider (CCSP), but CCSP usually does not have the information about the demand preference of users. In this paper, a contract model is adopted to address the cloud computing resource allocation and pricing problem in the mobile blockchain. In particular, an adverse selection contract solution is proposed to overcome the information asymmetry problem, and resource pooling is introduced to improve the stability of users rewards. Simulation results show that the information asymmetry problem is well overcome by adverse selection contract so that CCSP can obtain more utility than linear pricing contracts. Furthermore, the resource pooling could effectively improve the users and CCSPs utilities. When the size of the mining pool is large enough, it can achieve an improvement effect of more than 10 times. The effect of pool size and user type distribution on CCSPs utility is also studied.

Asset Pricing with Omitted Factors

Standard estimators of risk premia in linear asset pricing models are biased if some priced factors are omitted. We propose a three-pass method to estimate the risk premium of an observable factor, which is valid even when not all factors in the model are specified or observed. The risk premium of the observable factor can be identified regardless of the rotation of the other control factors if together they span the true factor space. Our approach uses principal components of test asset returns to recover the factor space and additional regressions to obtain the risk premium of the observed factor.

Future Stock Market Prediction Using Machine Learning

Stock market prediction using machine learning is highly effective to predict the future prices of the stock with minimum investment. This paper proposes the system that will predict the future prices of the stock of different companies this prediction will help a investor to take decisions to maximize profits. This paper shows that by using different techniques like support vector, LSTM, linear regression future prices of the stock can be effectively predicted.

With linear pricing, can profit‐maximizing monopoly output be socially efficient?

AbstractWe revisit the prevailing wisdom that a profit‐maximizing monopolist using linear pricing cannot produce socially efficient output. We show that when market demand function exhibits a flat portion, the prevailing wisdom may not be true. Such a “midway landing” in demand is consistent with weakly convex preferences, and many general demand functions such as any polynomials of degree three and higher. Thus, our analysis demonstrates that the output distortion resulting from linear pricing by a profit‐maximizing monopolist is demand specific. In general, neither monopoly per se nor linear pricing is the main reason for social inefficiency.

Oligopoly under incomplete information: On the welfare effects of price discrimination

We study competition by firms that simultaneously post (potentially nonlinear) tariffs to consumers who are privately informed about their tastes. Market power stems from informational frictions, in that consumers are heterogeneously informed about firms’ offers. In the absence of regulation, all firms offer quantity discounts. As a result, relative to Bertrand pricing, imperfect competition benefits disproportionately more consumers whose willingness to pay is high, rather than low. Regulation imposing linear pricing hurts the former but benefits the latter consumers. While consumer surplus increases, firms’ profits decrease, enough to drive down utilitarian welfare. By contrast, improvements in market transparency increase utilitarian welfare, and achieve similar gains on consumer surplus as imposing linear pricing, although with limited distributive impact. On normative grounds, our analysis suggests that banning price discrimination is warranted only if its distributive benefits have a weight on the societal objective.

Can Google Trends Improve Housing Market Forecasts?

We augment linear pricing models for the housing market commonly used in the literature with Google trends data in order to assess whether or not crowd-sourced search query data can improve the forecasting ability of the models. We estimate both sets of models (excluding and including the search query data) in order to assess statistical fit. We then compare various performance measures of the augmented linear model’s out-of-sample, dynamic forecasts against a baseline version. We find that augmenting the models to take advantage of the availability of Google trend data does not significantly improve the forecasting performance of the models.

Hedonic Index Numbers for Rents of Office and Shop Premises in Finland

The focus of the study is to join together regression analysis and index numbers to get quality adjusted price change for rents of office and shop premises. First, we apply simple semilogarithmic linear price models, the fixed effects model (FE), and estimate them by the OLS method. We weight these estimated equations from observations into stratums for unweighted and weighted arithmetic and geometric averages such that the basic algebraic properties of the OLS method are satisfied. We show that the aggregation leads to reparameterization of the FE’s (here stratum effects) of the OLS method for the unweighted and weighted arithmetic and the weighted geometric averages. The solution for the unweighted geometric average is trivial and shown in any statistical textbooks. Second, we apply the Oaxaca decomposition (1973) for the aggregated price models (i.e. stratum aggregates) for these four basic averages and divide the actual price change of these averages into two parts: into quality correction and quality adjusted price changes. For these Oaxaca decompositions of different averages, we apply index number theory to estimate price changes for crude aggregation levels. All our analysis, including the basic and excellent index number formulas (see Vartia and Suopera, 2018), are based on their logarithmic representations. Our focus for the use of the logarithmic representations culminates into the theorem of additive decomposition of the value change by which we can compare the price change estimates based on unit values (i.e. weighted arithmetic averages) and especially Montgomery-Vartia price index. We show explicitly that inadequate control of rented squares leads to serious bias – the actual price change includes not only price changes but also quantity changes, which may dominate causing serious bias for price index numbers. Our test data comes from the KTI Property Information Ltd covering large municipals in Finland. The data do not include certain ID-key for the construction of bilateral price-links and thus a hedonic method is our approach to measure price index for rents of office and shop premises. The weighting into the population level is at the moment impossible because lack of data, we make all inference only for the conditional information set of our data. All statistical and mathematical methods in this study are programmed by the SAS and the user interface for the official production of statistics by the SAS EG.