Local Parametric Analysis of Hedging in Discrete Time

P.L.M. Bossaerts, P. Hillion

Research output: Working paperDiscussion paperOther research output

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Abstract

When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41% for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18% for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ``smile'' effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ``wave'' effect in the relation with maturity for deep out-of-the-money options.
Original languageEnglish
PublisherCentER
Volume1995-23
Publication statusPublished - 1995

Publication series

NameCentER Discussion Paper
Volume1995-23

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Maturity
Hedging
Discrete-time
Tracking error
Black-Scholes
Parametric model
Discretization
Derivatives
Hedge
Hedge ratio
Smile
Black-Scholes model
Continuous time

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Bossaerts, P. L. M., & Hillion, P. (1995). Local Parametric Analysis of Hedging in Discrete Time. (CentER Discussion Paper; Vol. 1995-23). CentER.
Bossaerts, P.L.M. ; Hillion, P. / Local Parametric Analysis of Hedging in Discrete Time. CentER, 1995. (CentER Discussion Paper).
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title = "Local Parametric Analysis of Hedging in Discrete Time",
abstract = "When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41{\%} for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18{\%} for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ``smile'' effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ``wave'' effect in the relation with maturity for deep out-of-the-money options.",
author = "P.L.M. Bossaerts and P. Hillion",
year = "1995",
language = "English",
volume = "1995-23",
series = "CentER Discussion Paper",
publisher = "CentER",
type = "WorkingPaper",
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Bossaerts, PLM & Hillion, P 1995 'Local Parametric Analysis of Hedging in Discrete Time' CentER Discussion Paper, vol. 1995-23, CentER.

Local Parametric Analysis of Hedging in Discrete Time. / Bossaerts, P.L.M.; Hillion, P.

CentER, 1995. (CentER Discussion Paper; Vol. 1995-23).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Local Parametric Analysis of Hedging in Discrete Time

AU - Bossaerts, P.L.M.

AU - Hillion, P.

PY - 1995

Y1 - 1995

N2 - When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41% for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18% for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ``smile'' effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ``wave'' effect in the relation with maturity for deep out-of-the-money options.

AB - When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41% for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18% for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ``smile'' effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ``wave'' effect in the relation with maturity for deep out-of-the-money options.

M3 - Discussion paper

VL - 1995-23

T3 - CentER Discussion Paper

BT - Local Parametric Analysis of Hedging in Discrete Time

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Bossaerts PLM, Hillion P. Local Parametric Analysis of Hedging in Discrete Time. CentER. 1995. (CentER Discussion Paper).