An integral representation of elasticity and sensitivity for stochastic volatility models

Zhenyu Cui, Duy Nguyen, Hyungbin Park

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a generic probabilistic approach to study elasticities and sensitivities of financial quantities under stochastic volatility models. We describe the shock elasticity, the quantile sensitivity and the vega value of cash flows with respect to perturbation of the volatility function of the model. The main contribution is to establish explicit formulae for these elasticities and sensitivities based on a novel application of the exponential measure change technique in Palmowski and Rolski (Bernoulli 8(6):767–785 2002). We carry out explicit calculations for the Heston model and the 3/2 stochastic volatility model, and derive explicit expressions in terms of model parameters.

Original languageEnglish
Pages (from-to)249-274
Number of pages26
JournalMathematics and Financial Economics
Volume12
Issue number2
DOIs
StatePublished - 1 Mar 2018

Keywords

  • Elasticity
  • Exponential measure change
  • Greeks
  • Growth-rate risk
  • Quantile
  • Sensitivity
  • Stochastic volatility models

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