2020/03/19 by Peter Carr, Andrey Itkin, Carr, Peter +1 · 2 citations
Economics, Econometrics and Finance · Engineering · #Capital Investment and Risk Analysis #Stochastic processes and financial applications #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.2003.08853
In this paper we develop a semi-closed form solutions for the barrier (perhaps, time-dependent) and American options written on the underlying stock which follows a time-dependent OU process with a log-normal drift. This model is equivalent to the familiar Hull-White model in FI, or a time dependent OU model in FX. Semi-closed form means that given the time-dependent interest rate, continuous dividend and volatility functions, one need to solve numerically a linear (for the barrier option) or nonlinear (for the American option) Fredholm equation of the first kind. After that the option prices in all cases are presented as one-dimensional integrals of combination of the above solutions and Jacobi theta functions. We also demonstrate that computationally our method is more efficient than the backward finite difference method used for solving these problems, and can also be as efficient as the forward finite difference solver while providing better accuracy and stability.