Valuing discretely monitored barrier options

Options with the barrier feature are considered to be the simplest types of path dependent options.Barrier options distinctive feature is that the payoff depends not only on the final price of the underlyingasset, but also on whether the asset price has breached (one-touch) some barrier level duringthe life of the option. In this paper we explore the problem for pricing discrete barrier options utilizingthe Black-Scholes model for the random movement of the asset price. We postulate the problemas a path integral calculation by choosing approach that is similar to the quadrature method. Also,we perform a numerical algorithm for fast and accurate valuation of the multi-dimensional integralthat represents the formula for the double barrier option price. In addition, we present an error estimationof our approximation and derive for discrete barrier options an identity similar to the famousput-call parity. Our results for pricing discretely monitored one and double barrier options are inagreement with those obtained by other numerical and analytical methods in finance and literature.

Valuing discretely monitored barrier options Keywords:

Discrete barrier options , Black-Scholes model , Quadrature method , Multi-dimensional integral