Decisions in Economics and Finance

, Volume 42, Issue 2, pp 715–741 | Cite as

Semi-analytical prices for lookback and barrier options under the Heston model

  • Luca De Gennaro AquinoEmail author
  • Carole Bernard


Under the Heston stochastic volatility model, we derive semi-analytical formulas for the prices of path-dependent options with payoffs linked to the maximum or minimum value of the underlying asset price over a certain period of time. In particular, we obtain prices of lookback and barrier options in the Heston model, but the methodology applies more generally. By conditioning with respect to the variance path, we obtain pricing formulas that can be related to their counterparts in the Black–Scholes model.


Derivatives pricing Lookback options Barrier options Path-dependent options Heston model Stochastic volatility 

JEL Classification

C65 G13 



C. Bernard acknowledges the financial support of the Odysseus program of the FWO. We would like to thank François Desmoulins Lebeault, Gianluca Fusai, Lamya Kermiche and two anonymous referees for helpful comments.


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Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2019

Authors and Affiliations

  1. 1.Department of Accounting, Law and Finance, Grenoble Ecole de ManagementUniversité Grenoble Alpes ComUEGrenobleFrance
  2. 2.Department of Economics and Political SciencesVrije Universiteit Brussel (VUB)BrusselBelgium

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