Valuation of non-recourse stock loan using an integral equation approach

Abstract

An integral equation approach is adopted to price American-style non-recourse stock loans with finite maturities. In particular, we use Fourier transform to reduce the partial differential equation governing the price of an American-style non-recourse stock loan into an ordinary differential equation, the solution of which can be easily found (in the Fourier space) and analytically inverted into the original space. As a result, we can decompose the price of an American non-recourse stock loan into two main components: the price of its European counterpart and the early exit premium. This decomposition allows us to break the pricing problem of American stock loans into two simple steps: 1) finding the optimal exit prices; 2) calculating the American non-recourse stock loans. Our obtained numerical results appear to fit very well with those obtained from literature.