Barrier Options on Underlyings with Time-Dependent Parameters: A Perturbation Expansion Approach

17 Pages Posted: 3 Apr 2005 Last revised: 16 Dec 2015

Date Written: March 9, 2005

Abstract

In this paper we work out a perturbation expansion for the prices of barrier options on an underlying that follows a Black-Scholes dynamics with time-dependent parameters. It is to be considered as an extension of earlier work that provides, in a sense, a zero order approximation. Through an elegant argument we work out an easy numerical procedure by which a simple yet powerful correction to the average coefficients formulae commonly used yields prices that lie within basis points of the exact price of the option. The very important issue of Greeks bucketing is discussed as well by means of a numerical example, showing that this approach is viable for the effective management of option positions. This has important consequences on options trading particularly in the FX and credit derivatives markets.

Keywords: option pricing, Black--Scholes, barrier options, FX derivatives, credit derivatives, partial differential equations, perturbation theory

Suggested Citation

Rapisarda, Francesco, Barrier Options on Underlyings with Time-Dependent Parameters: A Perturbation Expansion Approach (March 9, 2005). Available at SSRN: https://ssrn.com/abstract=682184 or http://dx.doi.org/10.2139/ssrn.682184

Francesco Rapisarda (Contact Author)

Bloomberg L.P. ( email )

39 Finsbury Square
London, EC2A 1HD
United Kingdom

Register to save articles to
your library

Register

Paper statistics

Downloads
523
rank
49,913
Abstract Views
2,061
PlumX Metrics