Merton Model
Encyclopedia
The Merton model is a model proposed by Robert C. Merton
in 1974 for assessing the credit risk
of a company
by characterizing the company's equity as a call option
on its asset
s. Put-call parity is then used to price the value of a put and this is treated as an analogous representation of the firm's credit risk.
that will become due at a future time T. The company defaults
if the value of its assets is less than the promised debt repayment at time T. The equity of the company is a European call option
on the assets of the company with maturity T and a strike price equal to the face value of the debt. The model can be used to estimate either the risk-neutral probability that the company will default or the credit spread on the debt1.
The model takes three company specific inputs: the equity spot price, the equity volatility (which is transformed into asset volatility), and the debt/share. The model also takes two inputs which should be calibrated to market quoted CDS spreads: the default barrier, and the volatility of the default barrier. These inputs are used to specify a diffusion process for the asset value. The entity is deemed to have defaulted when the asset value drops below the barrier. The barrier itself is stochastic, which has the effect of incorporating jump-to-default risk into the model. The Merton model evolves asset value movements through a diffusion process and a fundamental purpose of the default barrier volatility is to provide a jump-like process which can capture short term default probabilities.
To calibrate model parameters, select a sample of credit spreads and iteratively adjust the model parameters to best match the market observed credit spreads using least-squared-error minimization. CreditGrades performed a calibration test in 2002 which determined the default barrier to be 0.5 and the default barrier vol to be 0.3 on an empirical market wide average basis. However, this study was performed during bull market conditions and may not represent the current state of the market nor a specific industrial sector. Subsequently, it is important to calibrate the model with respect to your industrial sector and the tenor of CDS spreads you wish to obtain.
spreads which are significantly higher than observed in the market due to the asset diffusion process.
Mertons model has been extended in a number of ways. For example, one version of the model assumes that a default occurs whenever the value of the assets fall below a barrier level.
Robert C. Merton
Robert Carhart Merton is an American economist, Nobel laureate in Economics, and professor at the MIT Sloan School of Management.-Biography:...
in 1974 for assessing the credit risk
Credit risk
Credit risk is an investor's risk of loss arising from a borrower who does not make payments as promised. Such an event is called a default. Other terms for credit risk are default risk and counterparty risk....
of a company
Company
A company is a form of business organization. It is an association or collection of individual real persons and/or other companies, who each provide some form of capital. This group has a common purpose or focus and an aim of gaining profits. This collection, group or association of persons can be...
by characterizing the company's equity as a call option
Call option
A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...
on its asset
Asset
In financial accounting, assets are economic resources. Anything tangible or intangible that is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset...
s. Put-call parity is then used to price the value of a put and this is treated as an analogous representation of the firm's credit risk.
Assumptions
This model assumes that a company has a certain amount of zero-coupon debtDebt
A debt is an obligation owed by one party to a second party, the creditor; usually this refers to assets granted by the creditor to the debtor, but the term can also be used metaphorically to cover moral obligations and other interactions not based on economic value.A debt is created when a...
that will become due at a future time T. The company defaults
Default (finance)
In finance, default occurs when a debtor has not met his or her legal obligations according to the debt contract, e.g. has not made a scheduled payment, or has violated a loan covenant of the debt contract. A default is the failure to pay back a loan. Default may occur if the debtor is either...
if the value of its assets is less than the promised debt repayment at time T. The equity of the company is a European call option
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American options. These options - as well as others where the...
on the assets of the company with maturity T and a strike price equal to the face value of the debt. The model can be used to estimate either the risk-neutral probability that the company will default or the credit spread on the debt1.
The model takes three company specific inputs: the equity spot price, the equity volatility (which is transformed into asset volatility), and the debt/share. The model also takes two inputs which should be calibrated to market quoted CDS spreads: the default barrier, and the volatility of the default barrier. These inputs are used to specify a diffusion process for the asset value. The entity is deemed to have defaulted when the asset value drops below the barrier. The barrier itself is stochastic, which has the effect of incorporating jump-to-default risk into the model. The Merton model evolves asset value movements through a diffusion process and a fundamental purpose of the default barrier volatility is to provide a jump-like process which can capture short term default probabilities.
To calibrate model parameters, select a sample of credit spreads and iteratively adjust the model parameters to best match the market observed credit spreads using least-squared-error minimization. CreditGrades performed a calibration test in 2002 which determined the default barrier to be 0.5 and the default barrier vol to be 0.3 on an empirical market wide average basis. However, this study was performed during bull market conditions and may not represent the current state of the market nor a specific industrial sector. Subsequently, it is important to calibrate the model with respect to your industrial sector and the tenor of CDS spreads you wish to obtain.
Accuracy
The Merton model has been shown to be empirically accurate for non-financial firms, especially manufacturing entities. The highly leveraged nature of financial firms produces CDSCredit default swap
A credit default swap is similar to a traditional insurance policy, in as much as it obliges the seller of the CDS to compensate the buyer in the event of loan default...
spreads which are significantly higher than observed in the market due to the asset diffusion process.
Mertons model has been extended in a number of ways. For example, one version of the model assumes that a default occurs whenever the value of the assets fall below a barrier level.