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Option Pricing with Discrete Rebalancing

Author

Listed:
  • Jean-Luc PRIGENT

    (THEMA, Université de Cergy-Pontoise)

  • Olivier RENAULT

    (Financial Markets Group, London School of Economics)

  • Olivier SCAILLET

    (HEC Genève and FAME, University of Geneva)

Abstract

We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after ¯xed relative changes in the stock price. The stock price follows a marked point process and the market is incomplete. We first characterisethe equivalent martingale measures. An explicit pricing formula based on the minimal martingale measure is then provided together with the hedging strategy underlying port-folio adjustments. Two examples illustrate our pricing framework : a jump process driven by a latent geometric Brownian motion and a marked Poisson process. We establish the convergence to the Black-Scholes model when the triggering price increment shrinks to zero. For the empirical application we use IBM, France Telecom and CAC 40 intraday transaction data, and compare option prices given by the marked Poisson model, the Black-Scholes model and observed option prices.

Suggested Citation

  • Jean-Luc PRIGENT & Olivier RENAULT & Olivier SCAILLET, 2002. "Option Pricing with Discrete Rebalancing," FAME Research Paper Series rp55, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp55
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    Cited by:

    1. is not listed on IDEAS
    2. 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), CY Cergy-Paris University, ESSEC and CNRS.
    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.

    More about this item

    Keywords

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    JEL classification:

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

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