A Continuity Correction for Discrete Barrier Options

A Continuity Correction for Discrete Barrier Options

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring in...

Continuity Correction for Barrier Options in Jump-Diffusion Models

Discrete Solutions for Barrier Options

A barrier option is an otherwise vanilla call or put option with a strike of X but with an extra parameter B, the barrier: the option only comes into existence (is knocked in) or is terminated (is knocked out) if the spot price crosses the barrier during the life of the option. Because there is a positive probability (in either case) of worthlessness, these options are cheaper than the correspo...

Discrete Barrier and Lookback Options

Discrete barrier and lookback options are among the most popular path-dependent options in markets. However, due to the discrete monitoring policy almost no analytical solutions are available for them. We shall focus on the following methods for discrete barrier and lookback option prices: (1) Broadie–Yamamoto method based on fast Gaussian transforms. (2) Feng–Linetsky method based on Hilbert t...

A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: barrier options

We discuss the ‘continuity correction’ that should be applied to relate the prices of discretely sampled barrier options and their continuouslysampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. We calculate the correction to higher order ...