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The Merton model primarily assesses default probability, which is a key aspect of credit risk management. It is a structural credit risk model that evaluates the likelihood of a company's default by analyzing the company's asset values in relation to its liabilities. The model operates on the premise that a company's equity can be viewed as a call option on its assets, and the default occurs when the value of the assets falls below the value of the liabilities at maturity.

By incorporating the volatility of the company's asset value and the debt structure, the Merton model provides an estimation of the probability that the company will be unable to meet its debt obligations. This focus on the likelihood of default makes it a vital tool for assessing credit risk, enabling lenders and investors to make informed decisions regarding loan pricing, investment strategy, and risk management.

In contrast, the other options—company profitability, market share, and debt-to-equity ratio—are important financial metrics but do not directly evaluate the likelihood of default in the same structured manner as the Merton model does. While they can provide insights into a company's overall financial health, they do not specifically address the risk of default that the Merton model is designed to assess.