# 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 language English 1450042 International Journal of Theoretical and Applied Finance 17 07 https://doi.org/10.1142/S0219024914500423 Published - 1 Nov 2014 Yes

### 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.",
keywords = "hedging risk, variance bounds, Least-squares Monte Carlo",
author = "Stefan Ankirchner and Christian Pigorsch and Nikolaus Schweizer",
year = "2014",
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doi = "10.1142/S0219024914500423",
language = "English",
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journal = "International Journal of Theoretical and Applied Finance",
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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

TY - JOUR

T1 - Estimating residual hedging risk with least-squares Monte Carlo

AU - Ankirchner, Stefan

AU - Pigorsch, Christian

AU - Schweizer, Nikolaus

PY - 2014/11/1

Y1 - 2014/11/1

N2 - 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.

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.

KW - hedging risk

KW - variance bounds

KW - Least-squares Monte Carlo

U2 - 10.1142/S0219024914500423

DO - 10.1142/S0219024914500423

M3 - Article

VL - 17

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

SN - 0219-0249

IS - 07

M1 - 1450042

ER -