### Local volatility changes in the Black-Scholes model

(2003) 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)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f9be7240-a2aa-4a1e-ad73-30c6dc519f16

- author
- Bermin, Hans-Peter
^{LU}and Kohatsu-Higa, Arturo - organization
- publishing date
- 2003
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Seminario de Matemática Financiera
- editor
- Menendez, Santiago Carrillo
- 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
- 2018-11-21 21:30:18

@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}, booktitle = {Seminario de Matemática Financiera}, editor = {Menendez, Santiago Carrillo}, isbn = {84-688-2450-X}, language = {eng}, pages = {113--134}, publisher = {Instituto MEFF}, title = {Local volatility changes in the Black-Scholes model}, url = {http://www.risklab.es/es/seminarios/bme-uam/Volumen03.pdf}, volume = {3}, year = {2003}, }