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.
|Title of host publication||Seminario de Matemática Financiera|
|Editors||Santiago Carrillo Menendez|
|Place of Publication||Madrid|
|Number of pages||22|
|Publication status||Published - 2003|
Subject classification (UKÄ)