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Option Pricing with Discrete Rebalancing

Author

Listed:
  • Prigent, J.-L.

    (Université de Cergy-Pontoise, THEMA)

  • Renault, O.

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

  • Scaillet, O.

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES); UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut d’Administration et de Gestion (IAG))

Abstract

We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after fixed relative variation of the stock price. The stock price follows a marked point process and the market is incomplete. We first characterize the equivalent martingale measures. An explicit formula based on the minimal martingale measure is then provided together with the hedging strategy underlying portfolio adjustments. Under adequate conditions on the stock price dynamics, the minimal pricing formula converges to the Black-Scholes formula when the triggering price increment shrinks to zero. This is shown theoretically and numerically on two examples : a marked Poisson process and a jump process driven by a latent geometric Brownian motion. For the empirical application we use IBM intraday transaction data and compare option prices given by the marked Poisson model and the Black-Scholes model.

Suggested Citation

  • Prigent, J.-L. & Renault, O. & Scaillet, O., 1999. "Option Pricing with Discrete Rebalancing," LIDAM Discussion Papers IRES 1999029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Oct 1999.
    • Handle: RePEc:ctl:louvir:1999029
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    References listed on IDEAS

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    Cited by:

    1. J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    3. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.

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    More about this item

    Keywords

    Weak convergence; incomplete markets; option pricing; minimal martingale measure; discrete rebalancing; marked point process;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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