Journal of Computational Finance

Risk.net

The condition of the integral representation of American Options

Pascal Heider

ABSTRACT

The pricing of an American option can be formulated as a free boundary problem for the Black–Scholes equation. If the free boundary is known, the option price can be evaluated by an integral representation involving the free boundary. Usually, the free boundary is approximated by some kind of numerical method, eg, as a solution of a suitable integral equation (Kim (1990); McKean (1965)) or a series expansion (Zhu (2006)). In this paper it is shown how the approximation error of the boundary influences the error in the option evaluation. A condition number κ depending only on the option parameters is introduced to measure this deviation.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

If you already have an account, please sign in here.

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: