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 languageEnglish
Pages (from-to)105-122
Number of pages18
JournalJournal of Computational Finance
Volume21
Issue number3
DOIs
Publication statusPublished - 2017 Dec 1

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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

Volatility risk structure for options depending on extrema. / Nakatsu, Tomonori.

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

Research output: Contribution to journalArticle

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