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Equal risk pricing and hedging of financial derivatives with convex risk measures

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  • Saeed Marzban
  • Erick Delage
  • Jonathan Yu-Meng Li

Abstract

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we establish that the problem reduces to solving independently the writer and the buyer's hedging problems with zero initial capital. By further imposing that the risk measures decompose in a way that satisfies a Markovian property, we provide dynamic programming equations that can be used to solve the hedging problems for both European and American options. All of our results are general enough to accommodate situations where the risk is measured according to a worst-case risk measure, as is typically done in robust optimization. Our numerical study illustrates the advantages of equal risk pricing over schemes that only account for a single party, pricing based on quadratic hedging (i.e. ϵ-arbitrage pricing), or pricing based on a fixed equivalent martingale measure (i.e. Black–Scholes pricing). In particular, the numerical results confirm that when employing an equal risk price both the writer and the buyer end up being exposed to risks that are more similar and on average smaller than what they would experience with the other approaches.

Suggested Citation

  • Saeed Marzban & Erick Delage & Jonathan Yu-Meng Li, 2022. "Equal risk pricing and hedging of financial derivatives with convex risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 47-73, January.
  • Handle: RePEc:taf:quantf:v:22:y:2022:i:1:p:47-73
    DOI: 10.1080/14697688.2021.1993614
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    Cited by:

    1. Parvin Malekzadeh & Zissis Poulos & Jacky Chen & Zeyu Wang & Konstantinos N. Plataniotis, 2024. "EX-DRL: Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning," Papers 2408.12446, arXiv.org, revised Aug 2024.
    2. Iuga, Iulia Cristina & Mudakkar, Syeda Rabab & Dragolea, Larisa Loredana, 2024. "Agricultural commodities market reaction to COVID-19," Research in International Business and Finance, Elsevier, vol. 69(C).
    3. Jussi Lindgren, 2023. "A Generalized Model for Pricing Financial Derivatives Consistent with Efficient Markets Hypothesis—A Refinement of the Black-Scholes Model," Risks, MDPI, vol. 11(2), pages 1-5, January.
    4. Ao Yang & Wenqi Li & Brian Sheng Xian Teo & Jaizah Othman, 2022. "The Impact of Financial Derivatives on the Enterprise Value of Chinese Listed Companies: Moderating Effects of Managerial Characteristics," IJFS, MDPI, vol. 11(1), pages 1-18, December.

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