asset follows a Geometric Brownian Motion process. Here we consider
a reduced-form credit risk model with the asset model as proposed
in Eq. (2.15). Let the lease be initiated at time t with maturity
s > t. Without the option, the defaultable lease rate is established
by the no-arbitrage argument of Eq. (3.4). If the lessee has the option
to purchase the asset at lease maturity at the fixed price K, the
lessee is effectively granted a European call on the asset with the
same maturity as the lease. Assuming the option price is rolled into
the lease rate, the expression for the arbitrage-free lease rate is
modified by adding to the right-hand side of Eq. (3.4) the annuitized
option term: