The Merton model, developed by

Robert C. Merton Robert Cox Merton (born July 31, 1944) is an American economist, Nobel Memorial Prize in Economic Sciences laureate, and professor at the MIT Sloan School of Management, known for his pioneering contributions to continuous-time finance, especia ...

in 1974, is a widely used

credit risk A credit risk is risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased ...

model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing the general possibility that it will go into credit default. Under this model, the value of stock equity is modeled as a

call option In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call option to exchange a security at a set price. The buyer of the call option has the right, but not the obligation, to buy an ...

on the value of the whole company – i.e. including the liabilities – struck at the nominal value of the liabilities; and the equity market value thus depends on the volatility of the market value of the company assets. The idea applied is that, in general, equity may be viewed as a call option on the firm: since the principle of

limited liability Limited liability is a legal status in which a person's financial liability is limited to a fixed sum, most commonly the value of a person's investment in a corporation, company or partnership. If a company that provides limited liability to it ...

protects equity investors, shareholders would choose not to repay the firm's debt where the value of the firm is less than the value of the outstanding debt; where firm value is greater than debt value, the shareholders would choose to repay – i.e. exercise their option – and not to liquidate. See . This is the first example of a "structural model", where bankruptcy is modeled using a microeconomic model of the firm's

capital structure In corporate finance, capital structure refers to the mix of various forms of external funds, known as capital, used to finance a business. It consists of shareholders' equity, debt (borrowed funds), and preferred stock, and is detailed in the ...

. Structural models are distinct from "reduced form models" – such as Jarrow–Turnbull – where bankruptcy is modeled as a statistical process. By contrast, the Merton model treats

bankruptcy Bankruptcy is a legal process through which people or other entities who cannot repay debts to creditors may seek relief from some or all of their debts. In most jurisdictions, bankruptcy is imposed by a court order, often initiated by the debtor ...

as a continuous

probability of default Probability of default (PD) is a financial term describing the likelihood of a default over a particular time horizon. It provides an estimate of the likelihood that a borrower will be unable to meet its debt obligations. PD is used in a variet ...

, where, on the random occurrence of default, the stock price of the defaulting company is assumed to go to zero.Robert Merton, "Option Pricing When Underlying Stock Returns are Discontinuous" ''Journal of Financial Economics'', 3, January–March, 1976, pp. 125–44. This microeconomic approach, to some extent, allows us to answer the question "what are the economic causes of default?"Nonlinear valuation and XVA under credit risk, collateral margins and Funding Costs
Prof. Damiano Brigo, UCLouvain

See also

References

Further reading