Title: Semi-analytical method for pricing barrier options with time-dependent parameters
Authors: Simona Sanfelici - University of Parma (Italy) [presenting]
Chiara Guardasoni - University of Parma (Italy)
Abstract: Barrier options are path-dependent derivatives that have become increasingly popular and frequently traded in the recent years. Closed-form pricing formulas for these contracts are available only under very special cases, such as in the Black-Scholes framework. Pricing of barrier option is traditionally based on Monte Carlo methods that are affected by high computational costs and inaccuracy due to their slow convergence or on PDE methods. We propose a stable, accurate and efficient numerical method for pricing barrier options in a model with time-dependent parameters. The new approach is based on the Boundary Element Method that was introduced in the Engineering field in 1970. Especially when the differential problem is defined in an unbounded domain and the data are assigned on a limited boundary (as for barrier options), the method is particularly advantageous for its high accuracy, for the implicit satisfaction of the far-field conditions at infinity and for the low discretization costs. This method has already been tested for the Black-Scholes and other stochastic volatility and jump-diffusion models, giving very good results in terms of accuracy and computational time. We think that the method could have a considerable range of applications that in these last years we started investigating.