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Superreplication of European multiasset derivatives with bounded stochastic volatility

Author

Listed:
  • Fausto Gozzi
  • Tiziano Vargiolu

Abstract

In this paper we analyze the superreplication approach in stochastic volatility models in the case of European multiasset derivatives. We prove that the Black-Scholes-Barenblatt (BSB) equation gives a superhedging strategy even if its solution is not twice differentiable. This is done under convexity assumptions on the final payoff h that are verified in some applications presented here. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Fausto Gozzi & Tiziano Vargiolu, 2002. "Superreplication of European multiasset derivatives with bounded stochastic volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 69-91, March.
    • Handle: RePEc:spr:mathme:v:55:y:2002:i:1:p:69-91
    DOI: 10.1007/s001860200172
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    Citations

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    Cited by:

    1. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
    2. Ryuichi Nakajima & Masayuki Kumon & Akimichi Takemura & Kei Takeuchi, 2010. "Approximations and asymptotics of upper hedging prices in multinomial models," Papers 1007.4372, arXiv.org, revised Jun 2011.
    3. repec:dau:papers:123456789/5374 is not listed on IDEAS
    4. Yansheng Ma & Yong Li, 2012. "A uniform asymptotic expansion for stochastic volatility model in pricing multi‐asset European options," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(4), pages 324-341, July.
    5. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    6. Cox, Alexander M.G. & Robinson, Benjamin A., 2023. "Optimal control of martingales in a radially symmetric environment," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 149-198.

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