How is the distance to default (DD) calculated when asset prices are lognormally distributed?
Understand the Problem
The question is asking about the method for calculating the distance to default (DD) when considering that asset prices follow a lognormal distribution. It's assessing knowledge of financial metrics and the specific formula associated with this calculation.
Answer
Use Merton model, Black-Scholes equations with asset's volatility, default point, and current value.
When assets are lognormally distributed, the Distance to Default (DD) is calculated using the Merton model. It involves using the Black-Scholes-Merton equations to relate the market value of equity and the asset's volatility, default point, and current asset value.
Answer for screen readers
When assets are lognormally distributed, the Distance to Default (DD) is calculated using the Merton model. It involves using the Black-Scholes-Merton equations to relate the market value of equity and the asset's volatility, default point, and current asset value.
More Information
The Merton model calculates the likelihood of a firm defaulting by treating its equity as a call option on its assets. The Distance to Default is a key indicator derived from structural models like Merton's.
Tips
A frequent mistake is incorrectly using the asset's value and volatility in the Black-Scholes model. Ensure the use of correct current market values and annualized volatilities.
Sources
- Probability by Using the Merton Model for Structural Credit Risk - in.mathworks.com
- Estimate Merton Distance-to-Default - Mingze Gao - mingze-gao.com
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