Calculating Default Probability using Reduced Form Models

In a reduced form credit risk model, default intensity, often modeled as a stochastic process, plays a critical role in determining the pricing of credit-sensitive instruments. Consider a firm whose default intensity, denoted by λ(t), follows an exponential distribution with a time-dependent intensity given by:

λ(t) = α + β * t

where α is the baseline default intensity and β is the sensitivity to time. Given that α = 0.02 and β = 0.005, calculate the default probability for this firm over a 3-year horizon using the integral of the default intensity function over this interval.