Annals of Finance

, Volume 14, Issue 2, pp 195–209 | Cite as

Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes

  • Vladislav Krasin
  • Ivan Smirnov
  • Alexander Melnikov
Research Article


This paper presents a methodology of finding explicit boundaries for some financial quantities via comparison of stochastic processes. The path-wise comparison theorem is used to establish domination of the stock price process by a process with a known distribution that is relatively simple. We demonstrate how the comparison theorem can be applied in the constant elasticity of variance model to derive closed-form expressions for option price bounds, an approximate hedging strategy and a conditional value-at-risk estimate. We also provide numerical examples and compare precision of our method with the distribution-free approach.


Stochastic differential equations Comparison theorem Option pricing Constant elasticity of variance model 

JEL Classification

C61 C63 G13 



The authors thank the anonymous referee and the editor for their valuable comments and suggestions to improve the paper. Research supported by the NSERC under Grant 5901.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Vladislav Krasin
    • 2
  • Ivan Smirnov
    • 3
  • Alexander Melnikov
    • 1
  1. 1.University of AlbertaEdmontonCanada
  2. 2.Barclays CapitalLondonUK
  3. 3.Susquehanna International GroupDublinIreland

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