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Option Pricing with Discrete Rebalancing

  • 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)

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.

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Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp55.

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Date of creation: Jul 2002
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Handle: RePEc:fam:rpseri:rp55
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  1. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  2. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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  7. Chesher, Andrew & Dhaene, Geert & Gouriéroux, Christian & Scaillet, Olivier, 1999. "Bartlett Identities Tests," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  8. Jean-Philippe Lesne & Jean-Luc Prigent & Olivier Scaillet, 1998. "Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates," Working Papers 98-51, Centre de Recherche en Economie et Statistique.
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  10. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
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  23. repec:fth:inseep:9932 is not listed on IDEAS
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