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A note on options and bubbles under the CEV model: implications for pricing and hedging

Author

Listed:
  • José Carlos Dias

    (Instituto Universitário de Lisboa (ISCTE-IUL)
    Business Research Unit (BRU-IUL))

  • João Pedro Vidal Nunes

    (Instituto Universitário de Lisboa (ISCTE-IUL)
    Business Research Unit (BRU-IUL))

  • Aricson Cruz

    (Instituto Universitário de Lisboa (ISCTE-IUL)
    Business Research Unit (BRU-IUL))

Abstract

The discounted price process under the constant elasticity of variance (CEV) model is not a martingale (wrt the risk-neutral measure) for options markets with upward sloping implied volatility smiles. The loss of the martingale property implies the existence of (at least) two option prices for the call option: the price for which the put-call parity holds and the (risk-neutral) price representing the lowest cost of replicating the call payoff. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.

Suggested Citation

  • José Carlos Dias & João Pedro Vidal Nunes & Aricson Cruz, 2020. "A note on options and bubbles under the CEV model: implications for pricing and hedging," Review of Derivatives Research, Springer, vol. 23(3), pages 249-272, October.
    • Handle: RePEc:kap:revdev:v:23:y:2020:i:3:d:10.1007_s11147-019-09164-x
    DOI: 10.1007/s11147-019-09164-x
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    More about this item

    Keywords

    Bubbles; CEV model; Greeks; Option pricing; Put-call parity; Local martingales;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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