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Tug-of-war, market manipulation and option pricing

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  • Kaj Nystrom
  • Mikko Parviainen

Abstract

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the non-linear and completely degenerate infinity Laplace operator.

Suggested Citation

  • Kaj Nystrom & Mikko Parviainen, 2014. "Tug-of-war, market manipulation and option pricing," Papers 1410.1664, arXiv.org.
    • Handle: RePEc:arx:papers:1410.1664
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    References listed on IDEAS

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