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On the stochastic elasticity of variance diffusions

Author

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  • Kim, Jeong-Hoon
  • Yoon, Ji-Hun
  • Lee, Jungwoo
  • Choi, Sun-Yong

Abstract

The elasticity of variance of risky assets has been observed to be rapidly fluctuating around a level. The level itself slowly varies depending upon the corresponding economic situation at the time of consideration. In particular, it turns out to be extraordinary during the peak period of the 2007–2009 Global Financial Crisis. Based on the concept of stochastic elasticity of variance, this paper develops an asset price model in a multiscale form and applies it to the pricing of European options and verifies a significant improvement over the constant elasticity of variance model in terms of the geometric structure (skew or smirk) of implied volatility. Our result implies that a theoretical model based on the random elasticity can derive market's volatility forecast more accurately than the constant elasticity so that investors can employ a dynamic investment strategy reducing risk more effectively.

Suggested Citation

  • Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
    • Handle: RePEc:eee:ecmode:v:51:y:2015:i:c:p:263-268
    DOI: 10.1016/j.econmod.2015.08.011
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    References listed on IDEAS

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    Cited by:

    1. Marcos Escobar-Anel & Weili Fan, 2023. "The SEV-SV Model—Applications in Portfolio Optimization," Risks, MDPI, vol. 11(2), pages 1-34, January.
    2. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    3. Min-Ku Lee, 2019. "Pricing Perpetual American Lookback Options Under Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1265-1277, March.
    4. Kim, Donghyun & Choi, Sun-Yong & Yoon, Ji-Hun, 2021. "Pricing of vulnerable options under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Xia, Kun & Yang, Xuewei & Zhu, Peng, 2023. "Delta hedging and volatility-price elasticity: A two-step approach," Journal of Banking & Finance, Elsevier, vol. 153(C).
    6. Min-Ku LEE & Sung-Jin YANG, PhD & Jeong-Hoon KIM, 2017. "Pricing Vulnerable Options with Constant Elasticity of Variance versus Stochastic Elasticity of Variance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 233-247.
    7. Cao, Jiling & Kim, Jeong-Hoon & Kim, See-Woo & Zhang, Wenjun, 2020. "Rough stochastic elasticity of variance and option pricing," Finance Research Letters, Elsevier, vol. 37(C).
    8. Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    9. Yoon, Ji-Hun & Park, Chang-Rae, 2016. "Pricing turbo warrants under stochastic elasticity of variance," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 107-118.
    10. Seo, Jun-Ho & Kim, Jeong-Hoon, 2022. "Multiscale stochastic elasticity of variance for options and equity linked annuity; A Mellin transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 303-320.
    11. Cao, Jiling & Kim, Jeong-Hoon & Li, Xi & Zhang, Wenjun, 2023. "Valuation of barrier and lookback options under hybrid CEV and stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 660-676.
    12. Kim, Donghyun & Shin, Yong Hyun & Yoon, Ji-Hun, 2024. "The valuation of real options for risky barrier to entry with hybrid stochastic and local volatility and stochastic investment costs," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    13. Kim, Donghyun & Ha, Mijin & Kim, Jeong-Hoon & Yoon, Ji-Hun, 2024. "A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).

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