# Volatility risk structure for options depending on extrema

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In this paper, we give a decomposition formula to calculate the vega index (sensitivity with respect to changes in volatility) for options with prices that depend on the extrema (maximum or minimum) and terminal value of the underlying stock price; this is assumed to follow a one-dimensional perturbed diffusion process. As a numerical application, we compute the vega index for lookback, European and up-in call options under the Black-Scholes model perturbed with a constant elasticity of variance modeltype perturbation. We compare these values with the standard nonperturbed Black-Scholes model, which, interestingly, turn out to be very different.

Original language English 105-122 18 Journal of Computational Finance 21 3 https://doi.org/10.21314/JCF.2017.334 Published - 2017 Dec 1

### Fingerprint

Elasticity
Decomposition
Black-Scholes model
Volatility risk
Vega
Stock prices
Call option
Diffusion process
Perturbation

### Keywords

• Barrier option
• Lookback option
• Malliavin calculus
• Stochastic differential equation
• Vega

### ASJC Scopus subject areas

• Finance
• Computer Science Applications
• Applied Mathematics

### Cite this

In: Journal of Computational Finance, Vol. 21, No. 3, 01.12.2017, p. 105-122.

Research output: Contribution to journalArticle

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