Estimating residual hedging risk with least-squares Monte Carlo

Stefan Ankirchner, Christian Pigorsch, Nikolaus Schweizer

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.
Original languageEnglish
Article number1450042
JournalInternational Journal of Theoretical and Applied Finance
Volume17
Issue number07
DOIs
Publication statusPublished - 1 Nov 2014
Externally publishedYes

Fingerprint

Hedging
Least-squares Monte Carlo
Hedging strategies
Diffusion model
Basis risk
Approximation
Intrinsic
Dynamic hedging
Estimator
Risk exposure

Keywords

  • hedging risk
  • variance bounds
  • Least-squares Monte Carlo

Cite this

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title = "Estimating residual hedging risk with least-squares Monte Carlo",
abstract = "Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.",
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Estimating residual hedging risk with least-squares Monte Carlo. / Ankirchner, Stefan; Pigorsch, Christian; Schweizer, Nikolaus.

In: International Journal of Theoretical and Applied Finance, Vol. 17, No. 07, 1450042, 01.11.2014.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Ankirchner, Stefan

AU - Pigorsch, Christian

AU - Schweizer, Nikolaus

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AB - Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.

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KW - variance bounds

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