Estimating Structural Models of Corporate Bond Prices

One of the strengths of structural models (or firm-value based models) of credit (e.g. Merton, 1974) as opposed to reduced-form models (e.g. Jarrow and Turnbull, 1995) is that they directly link the price of equity to default probabilities, and hence to the price of corporate bonds (and credit derivatives). Yet when these models are estimated on actual data, the existence of data other than equity prices is typically ignored. This paper describes how all available price data (equity prices, bond prices, possibly credit derivative prices) can be used in estimation, and illustrates that using e.g. bond price data in addition to equity price data greatly improves estimates. In this context, the issue of possibly noisy data and/or model error is also discussed.