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ELS pricing and hedging in a fractional Brownian motion environment

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  • Kim, Seong-Tae
  • Kim, Hyun-Gyoon
  • Kim, Jeong-Hoon

Abstract

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.

Suggested Citation

  • Kim, Seong-Tae & Kim, Hyun-Gyoon & Kim, Jeong-Hoon, 2021. "ELS pricing and hedging in a fractional Brownian motion environment," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308456
    DOI: 10.1016/j.chaos.2020.110453
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    Cited by:

    1. Sangkwon Kim & Jisang Lyu & Wonjin Lee & Eunchae Park & Hanbyeol Jang & Chaeyoung Lee & Junseok Kim, 2024. "A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2069-2086, May.
    2. Kim, Hyun-Gyoon & Kim, See-Woo & Kim, Jeong-Hoon, 2024. "Variance and volatility swaps and options under the exponential fractional Ornstein–Uhlenbeck model," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
    3. Soobin Kwak & Youngjin Hwang & Yongho Choi & Jian Wang & Sangkwon Kim & Junseok Kim, 2022. "Reconstructing the Local Volatility Surface from Market Option Prices," Mathematics, MDPI, vol. 10(14), pages 1-12, July.

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