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Option Pricing with Discrete Rebalancing

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  • Jean -Luc Prigent

    (Crest)

  • Olivier Renault

    (Crest)

  • Olivier Scaillet

    (Crest)

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.
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  • Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "Option Pricing with Discrete Rebalancing," Working Papers 99-61, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:99-61
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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. 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.
    3. 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.

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    More about this item

    JEL classification:

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

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