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Local volatility changes in the Black-Scholes model

Bermin, Hans-Peter LU and Kohatsu-Higa, Arturo (2003) In Seminario de Matemática Financiera 3. p.113-134
Abstract
In this paper we address a sensitivity problem with financial applications. Namely the study of price variations of different contingent claims in the Black-Scholes model due to changes in volatility. This study needs an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, which we call the local Vega index (lvi). This index measures the importance of a volatility perturbation at a certain point in time. We compute this index for different options and conclude that for the contingent claims studied in this paper, the lvi can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the... (More)
In this paper we address a sensitivity problem with financial applications. Namely the study of price variations of different contingent claims in the Black-Scholes model due to changes in volatility. This study needs an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, which we call the local Vega index (lvi). This index measures the importance of a volatility perturbation at a certain point in time. We compute this index for different options and conclude that for the contingent claims studied in this paper, the lvi can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the lvi is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and conclude that the speed of convergence is in fact related to the lvi. (Less)
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author
organization
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Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Seminario de Matemática Financiera
editor
Menendez, Santiago Carrillo and
volume
3
pages
22 pages
publisher
Instituto MEFF
ISBN
84-688-2450-X
language
English
LU publication?
yes
id
f9be7240-a2aa-4a1e-ad73-30c6dc519f16
alternative location
http://www.risklab.es/es/seminarios/bme-uam/Volumen03.pdf
date added to LUP
2017-03-01 19:03:24
date last changed
2017-03-08 10:05:41
@inbook{f9be7240-a2aa-4a1e-ad73-30c6dc519f16,
  abstract     = {In this paper we address a sensitivity problem with financial applications. Namely the study of price variations of different contingent claims in the Black-Scholes model due to changes in volatility. This study needs an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, which we call the local Vega index (lvi). This index measures the importance of a volatility perturbation at a certain point in time. We compute this index for different options and conclude that for the contingent claims studied in this paper, the lvi can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the lvi is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and conclude that the speed of convergence is in fact related to the lvi.},
  author       = {Bermin, Hans-Peter and Kohatsu-Higa, Arturo},
  editor       = {Menendez, Santiago Carrillo},
  isbn         = {84-688-2450-X},
  language     = {eng},
  pages        = {113--134},
  publisher    = {Instituto MEFF},
  series       = {Seminario de Matemática Financiera},
  title        = {Local volatility changes in the Black-Scholes model},
  volume       = {3},
  year         = {2003},
}