Abstract:
This paper develops an efficient simulation-based method to price derivative securities whose payoff depends on a first-passage time and the value of its underlying at that time, under the assumption that the underlying’s process follows the jump-diffusion model. Because of the high variation of payoff and the rarity of the first-passage event, pricing such securities using Monte Carlo simulation is challenging, and usually results in a price estimate that has high variance. As a solution, we devise an improved method for pricing such securities by combining three techniques: partitioning, exponential twisting, and conditional Monte Carlo. We provide an analysis of the proposed method and derive an approximation for the second moment of the resulting price estimate. In our numerical experiments, we consider Contingent Convertible bonds as an example to demonstrate the effectiveness of the proposed method in reducing the variance of the price estimate. Numerical results show that the proposed method, with parameters selected through simple criteria laid out in the analysis, provides substantial variance reduction.
