The Heston model with stochastic elasticity of variance

Sun Yong Choi, Jeong-Hoon Kim, Ji Hun Yoon

Research output: Contribution to journalArticle

Abstract

Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in-the-money and out-of-the-money) of time-to-maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface.

Original languageEnglish
Pages (from-to)804-824
Number of pages21
JournalApplied Stochastic Models in Business and Industry
Volume32
Issue number6
DOIs
Publication statusPublished - 2016 Nov 1

Fingerprint

Heston Model
Skew
Elasticity
Stochastic Volatility
Volatility
Implied Volatility
European Options
Ergodic Theory
Stochastic Volatility Model
Tractability
Factor Models
Hybrid Model
Asymptotic Analysis
Discrepancy
Asymptotic analysis
Closed-form
Time Scales
Stochastic models
Range of data
Heston model

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Business, Management and Accounting(all)
  • Management Science and Operations Research

Cite this

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The Heston model with stochastic elasticity of variance. / Choi, Sun Yong; Kim, Jeong-Hoon; Yoon, Ji Hun.

In: Applied Stochastic Models in Business and Industry, Vol. 32, No. 6, 01.11.2016, p. 804-824.

Research output: Contribution to journalArticle

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