Managing Hedge Fund Risk and Financing: Adapting to a New Era

Structural default Model

Structural-default models, such as the Merton Model, have been shown to be empirically accurate for non-financial firms, especially manufacturing entities. However, for highly leveraged financial firms, structural models predict credit spreads which are significantly higher than those observed in the market because of the high volatility of their assets and liabilities compared to those of less-levered non-financial firms. While not directly applicable to the measurement of the default probability of hedge funds, structural default models can provide a useful framework for considering that probability.

Structural models take three specific inputs: net asset value, the volatility of net asset value, and the value of liabilities/equity. The model also takes two inputs: the default barrier, and the volatility of the default barrier. These inputs are used to specify a diffusion process for the asset value. An 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. Structural default models evolve 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.

Hedge funds have assets and liabilities. Liabilities are primarily debits owed to prime brokers to repay margin loans. Equity is contributed ...