Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge

We develop a numerical algorithm for predicting prices and Greeks of equity-linked securities (ELS) with a knock-in barrier at any time over the total time period from issue date to maturity by using Monte Carlo simulation (MCS). The ELS is one of the most important financial derivatives in Korea. In the proposed algorithm, first we calculate the probability (0 ≤ p ≤ 1 {0\leq p\leq 1}) that underlying asset price never hits the knock-in barrier up to the intermediate evaluation date. Second, we compute two option prices V n k {V{nk}} and V k {V{k}}, where V_nk {V{nk}} is the option value which knock-in event does not occur and V k {V{k}} is the option value which knock-in event occurs. Finally, we predict the option value with a weighted average. We apply the proposed algorithm to two- and three-asset ELS. We provide the pseudo-numerical algorithm and computational results to demonstrate the usefulness of the proposed method.