The goal of the first part of the chapter is to show the methods of using R for pricing and performing Monte Carlo simulations with standard credit risk models. The following sections give an essential picture of loss distributions and the generating and pricing of a single debt instrument.
We start with the well-known option-based model of Merton (Merton 1974) as the introductory model of structural approach. Merton evaluates risky debt as a contingent claim of the firm value. Let us suppose that the
V firm value follows geometric Brownian motion:
In the preceding formula,
μ is the drift parameter,
σ>0 is the volatility parameter,
dW is the differential of the Wiener process, and the initial asset value is
V0>0. The model assumes a flat yield curve, with
r as the constant interest rate, and lets us define the default state as that where the value of the assets V falls below the liabilities (
K) upon the of maturity of debt (T). We express the VT...