Option pricing with discrete rebalancing
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.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Jean-Paul Laurent & Olivier Scaillet, 1999. "Variance Optimal Cap Pricing Models," Working Papers 99-07, Centre de Recherche en Economie et Statistique.
- Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
- N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
- David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
- Fabio Mercurio & Ton Vorst, 1996. "Option pricing with hedging at fixed trading dates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(2), pages 135-158.
- Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
- Runggaldier, Wolfgang J. & Martin Schweizer, 1995. "Convergence of Option Values under Incompleteness," Discussion Paper Serie B 333, University of Bonn, Germany.
- 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.
- Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
- Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298.
- Bouleau, Nicolas & Lamberton, Damien, 1989. "Residual risks and hedging strategies in Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 131-150, October.
- Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
- Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
- O. Scaillet & J.-L. Prigent & J.-P. Lesne, 2000. "Convergence of discrete time option pricing models under stochastic interest rates," Finance and Stochastics, Springer, vol. 4(1), pages 81-93.
- 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.
- Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- repec:crs:wpaper:9932 is not listed on IDEAS
- Hua He & William P. Keirstead & Joachim Rebholz, 1998. "Double Lookbacks," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 201-228.
- Hua He William P. Keirstead and Joachim Rebholz., 1995. "Double Lookbacks," Research Program in Finance Working Papers RPF-248, University of California at Berkeley.
- 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 637-654, May-June.
- Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
- 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).
- Andrew Chesher & Geert Dhaene & Christian Gourieroux & Olivier Scaillet, 1999. "Bartlett Identities Tests," Working Papers 99-32, Centre de Recherche en Economie et Statistique.
- CHESHER, Andrew & DHAENE, Geert & GOURIEROUX, Christian & SCAILLET, Olivier, 1999. "Bartlett identities tests," CORE Discussion Papers 1999039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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. Full references (including those not matched with items on IDEAS)