The Theoretical Price of a Share-Based Payment with Performance Conditions and Implications for the Current Accounting Standards

TL;DR

This paper develops a theoretical model for pricing share-based payments with performance conditions, addressing gaps in current standards and providing a practical, parameter-efficient approach for improved valuation accuracy.

Contribution

It introduces a marginal utility-based pricing model for SPPC, explicitly links performance variables to stock betas, and offers estimation methods to enhance current accounting standards.

Findings

The model demonstrates how to change probability distributions for variables affecting SPPC payoff.

It links performance variable drifts to stock betas under changed probabilities.

The approach uses few parameters, facilitating practical application.

Abstract

Although the growth of share-based payments with performance conditions (hereafter, SPPC) is prominent today, the theoretical price of SPPC has not been sufficiently studied. Reflecting such a situation, the current accounting standards for share-based payments issued in 2004 have had many problems. This paper develops a theoretical SPPC price model with a framework for a marginal utility-based price, which previous studies proposed is the price of contingent claims in an incomplete market. This paper's contribution is fivefold. First, we restricted the stochastic process to a certain class to demonstrate how to consistently change all variables' probability distributions, which affect the SPPC payoff. Second, we explicitly indicated not only the stochastic processes of the stock price process and performance variables under the changed probability, but also how the changes in the performance variables' drift coefficients related to stock betas. Third, we proposed a convenient model in application that uses only a few parameters. Fourth, we provided a method to estimate the parameters and improve the estimation of both the price and parameters. Fifth, we illustrated the problems in current accounting standards and indicated how the theoretical price model can significantly improve them.