Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier

25 Pages Posted: 30 Jul 2009

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Robert Tang

University of Melbourne - Centre for Actuarial Studies

Date Written: July 30, 2009

Abstract

We develop new Monte Carlo techniques based on stratifying the stock's hitting-times to the barrier for the pricing and Delta calculations of discretely-monitored barrier options using the Black-Scholes model. We include a new algorithm for sampling an Inverse Gaussian random variable such that the sampling is restricted to a subset of the sample space. We compare our new methods to existing Monte Carlo methods and find that they can substantially improve convergence speeds.

Keywords: first-hitting time, passage times, hitting-times, barrier, discretely-monitored, inverse Gaussian, stratified sampling, Monte-Carlo

Suggested Citation

Joshi, Mark and Tang, Robert, Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier (July 30, 2009). Available at SSRN: https://ssrn.com/abstract=1441142 or http://dx.doi.org/10.2139/ssrn.1441142

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies (deceased) ( email )

Melbourne, 3010
Australia

Robert Tang

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

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