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2009•Unpublished venueRequires access

Sensitivity analysis for barrier options

Yongqiang Wang, Michael C. Fu, Steven I. Marcus

Open publisher page 8 citations

Abstract

Barrier options are popular derivative securities with payoffs dependent on whether or not an underlying asset crosses a barrier. This paper presents a Monte Carlo simulation-based method of sensitivity analysis for barrier options based on smoothed perturbation analysis (SPA) for a general form of discontinuous sample function payoffs. The connection between the resulting SPA estimator and the probability formula derived in Hong (2008) and its generalization in Liu and Hong (2009) is explored. Using a Brownian bridge result, the estimator is applied to continuously-monitored barrier options with rebates. Illustrative simulation examples are provided. 1

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What this paper is about

Barrier options are popular derivative securities with payoffs dependent on whether or not an underlying asset crosses a barrier. This paper presents a Monte Carlo simulation-based method of sensitivity analysis for barrier options based on smoothed perturbation analysis (SPA) for a general form of discontinuous sample function payoffs. The connection between the resulting SPA estimator and the probability formula derived in Hong (2008) and its generalization in Liu and Hong (2009) is explored. Using a Brownian bridge result, the estimator is applied to continuously-monitored barrier options with rebates. Illustrative simulation examples are provided. 1

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Available abstract

Barrier options are popular derivative securities with payoffs dependent on whether or not an underlying asset crosses a barrier. This paper presents a Monte Carlo simulation-based method of sensitivity analysis for barrier options based on smoothed perturbation analysis (SPA) for a general form of discontinuous sample function payoffs. The connection between the resulting SPA estimator and the probability formula derived in Hong (2008) and its generalization in Liu and Hong (2009) is explored. Using a Brownian bridge result, the estimator is applied to continuously-monitored barrier options with rebates. Illustrative simulation examples are provided. 1

Key concepts: Barrier option, Brownian bridge, Estimator, Monte Carlo method, Sensitivity (control systems), Generalization, Applied mathematics, Exotic option

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