A simple lattice approximation for skew diffusions

This study proposes a recombining lattice-based methodology useful to discretize skew diffusions that allow to capture more accurately the dynamics of the underlying activity, i.e., stock prices in finance or reference funds in actuarial markets, thus overcoming the biases introduced by the Black-Scholes model. The lattice-based discretization is flexible and applicable to a wide range of skew diffusions and is suitable for evaluating financial derivatives, bonds, and interest-sensitive claims, particularly, when American-style contracts are considered. In this perspective, it is useful not only in financial but also in actuarial applications where such claims are embedded in several structured insurance policies, e.g., equity-linked policies with surrender options. The proposed binomial lattice model is generated directly starting from the original skew process, which is made piecewise tractable by simply applying the Harrison-Shepp methodology to manage the local time component. The method is able to force a heteroskedastic process to be homoskedastic to obtain a recombinant and computationally simple lattice in which the number of nodes grows up linearly with the number of time steps. The lattice is constructed starting from the computation of the node values on the edges, while the values for the inner nodes are simply determined by generating horizontal layers of nodes starting from the ones located on the two edges. Transition probabilities are computed by imposing that the two successor points for each node bracket the expected process value in the next time interval. Numerical comparisons with the existing models show that the proposed approach is accurate and efficient, and recovers various benchmark results in the literature when applied to evaluate European and American call and put options, equity-linked policies with or without surrender options, bonds, and interest-sensitive claims.