Merton Model

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 assets. 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.^[1]

Assumptions

This model assumes that a company has a certain amount of zero-coupon debt 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.

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 CDS 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.

See also

• Black–Scholes
• Jarrow–Turnbull model
• Default risk

References

1. ^ John Hull, Izzy Nelken, and Alan White (2004): "Merton's Model, Credit Risk and Volatility Skews", Journal of Credit Risk, Vol. 1, No. 1, pp. 3-28, Winter 2004/05