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Option pricing with discrete rebalancing

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  • Prigent, Jean-Luc
  • Renault, Olivier
  • Scaillet, Olivier

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 11 (2004)
Issue (Month): 1 (January)
Pages: 133-161

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Handle: RePEc:eee:empfin:v:11:y:2004:i:1:p:133-161

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Web page: http://www.elsevier.com/locate/jempfin

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  1. Laurent, J.P. & Scaillet, O., 1997. "Variance Optimal Cap Pricing Models," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 01 Jan 1999.
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  12. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
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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.

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