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Stochastic arbitrage with market index options

Author

Listed:
  • Beare, Brendan K.
  • Seo, Juwon
  • Zheng, Zhongxi

Abstract

Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed-integer linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, finding no evidence that stochastic arbitrage opportunities are systematically present. A skewed specification of the underlying market return distribution with a constant market risk premium and constant multiplicative variance risk premium is broadly consistent with the pricing of market index options at moderate strikes.

Suggested Citation

  • Beare, Brendan K. & Seo, Juwon & Zheng, Zhongxi, 2025. "Stochastic arbitrage with market index options," Journal of Banking & Finance, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:jbfina:v:173:y:2025:i:c:s0378426625000160
    DOI: 10.1016/j.jbankfin.2025.107395
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    Keywords

    Linear program; Mixed-integer linear program; Option mispricing; Portfolio choice; Pricing kernel puzzle; Stochastic arbitrage; Stochastic dominance;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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