A simple and efficient numerical method for pricing discretely monitored early-exercise options.

• Many popular exotic options are path-dependent and have early-exercise features. • Most path-dependent exotic options are discretely monitored and need to be priced using numerical techniques. • Traditional pricing methods such as Monte-Carlo simulations or finite difference methods are easy to implement but are often too slow. • More advanced pricing methods tend to be more efficient but are often too difficult to understand and to properly implement. • Our new quadrature-based method is very efficient while at the same time is very easy to understand and implement. We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is O (1 / N 4) and the complexity is O (M N log N) , where N is the number of grid points and M is the number of observation dates. Besides Black-Scholes, our method is also applicable to more general frameworks such as Merton's jump diffusion model. [ABSTRACT FROM AUTHOR]