Linear Valuation Models Research Articles

Distribution-Free Contextual Dynamic Pricing

Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer’s valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer’s true valuation, but instead needs to learn the valuation by leveraging contextual information and historic binary purchase feedback. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the linear valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, in which a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sublinear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto loan data set. Funding: Y. Liu and W.W. Sun acknowledge support from the National Science Foundation Division of Social and Economic Sciences [Grant NSF-SES 2217440]. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/moor.2023.1369 .

Analysing the market–book value relation in large Australian and US firms: implications for fundamental analysis and the market–book ratio

AbstractThis study compares the market–book relation of Australian and US firms using firm‐level dynamic analysis of using annual data for a long‐run period in error correction modelling. This paper contributes to a recent call for alternative ways of estimating Ohlson‐type linear valuation models (Ohlson and Kim, 2015). Log transformations of the data are used in this study to improve the statistical properties of the models. This study contributes to the findings on linear valuation model estimation for long‐run firms. Based on the returns model estimation, we find evidence of a higher level of co‐integration between market and book values for Australian firms.

Interpretability of Empirical Valuation Models in the Value Relevance Literature

This paper proposes an alternative formulation of the information dynamics that can serve as a foundation for the linear valuation models tested in empirical research. The models tested in the literature express market value either as a function of earnings and equity book value (net income form) or residual income and equity book value (residual income form). The net income form deviates from its theoretical development by excluding either current dividends or prior equity book value. The current formulation is consistent with the valuation models tested in the literature, and without the need to include a discount rate. The current study provide expectations on the regression coefficients produced from the empiricist's tests. Finally, since model selection is fundamentally an empirical question, we propose a model specification test for choosing among modeling alternatives.

Multi-Lagged Specification of the Ohlson Model

This paper extends the study by Bar-Yosef, Callen, and Livnat (BCL) (1996), in which they test the single lagged formulation of the Ohlson (1995) linear valuation model by assuming that book values, earnings, and dividends are the underlying primitives in a multi-lagged Garman-Ohlson (1980) framework. Unlike BCL who focus solely on the information dynamic, this paper estimates both the information dynamic and the valuation equation. Also, since Akaike's (1969a, 1969b) final prediction error (FPE) and Akaike's (1973, 1974) information criterion (AIC) are known to overfit in small samples, the lag structure specification in this study is estimated by the AICe criterion suggested by Hurvich and Tsai (1989, 1991, 1994) rather than by the FPE criterion of BCL. Furthermore, to bias the case against a multi-lagged structure, the maximum lag structure is limited to three lags per variable rather than the five lags of BCL. Utilizing the result that the lag structure of the information dynamic determines the lag structure of the valuation equation, the internal consistency of the model is evaluated from the estimated lag structures. The median lag structure for the valuation equation implied by the lag structure of the estimated information dynamic is found to be somewhat inconsistent with the median lag structure estimated directly from the valuation equation. Further testing on a stationary subsample suggests that the inconsistency may be induced by nonstationarities. Overall, the results indicate strongly that the modeling of earnings and book values in a linear valuation framework necessarily requires a multi-lagged formulation rather than the single lag formulation common to the empirical accounting literature.

Linear Valuation Models in Continuous Time with Accounting Information

Linear Valuation Models in Continuous Time with Accounting Information

Historical Cost Accrual Methods and the Role of Book Value and Earnings in Linear Valuation Models

Historical Cost Accrual Methods and the Role of Book Value and Earnings in Linear Valuation Models