ELS pricing and hedging in a fractional Brownian motion environment

Seong Tae Kim, Hyun Gyoon Kim, Jeong Hoon Kim

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1 Citation (Scopus)


An equity-linked security (ELS) is a debt instrument with several payments and maturities linked to equity markets. This paper is a study of the pricing and hedging of the ELS when the underlying asset price moves in a geometric fractional Brownian motion environment. We develop two different methods for calibrating fractional implied volatility, obtain an empirical result on the Hurst exponent, and introduce a new Greek called Eta to find the sensitivity of the ELS price to the Hurst parameter. We propose three Delta hedging strategies and compare them with each other and the classical Black-Scholes Delta hedging strategy. Their performance is shown to depend on market circumstance (bull or bear). Our results with constant volatility and Hurst exponent provide a building basis for more stable hedging strategies in the non-Markov environment.

Original languageEnglish
Article number110453
JournalChaos, Solitons and Fractals
Publication statusPublished - 2021 Jan

Bibliographical note

Funding Information:
The research of J.-H. Kim was supported by the National Research Foundation of Korea NRF2020R1H1A2006105 .

Publisher Copyright:
© 2020 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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