Local volatility changes in the Black-Scholes model

Hans-Peter Bermin, Arturo Kohatsu-Higa

Research output: Chapter in Book/Report/Conference proceedingBook chapter

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.
Original languageEnglish
Title of host publicationSeminario de Matemática Financiera
EditorsSantiago Carrillo Menendez
Place of PublicationMadrid
PublisherInstituto MEFF
Pages113-134
Number of pages22
Volume3
ISBN (Electronic)84-688-2450-X
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Economics

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