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A parsimonious model for intraday European option pricing

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  • Enrico Scalas
  • Mauro Politi

Abstract

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.

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File URL: http://arxiv.org/pdf/1202.4332
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Paper provided by arXiv.org in its series Papers with number 1202.4332.

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Date of creation: Feb 2012
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Handle: RePEc:arx:papers:1202.4332

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  1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
  4. Miquel Montero, 2007. "Renewal equations for option pricing," Papers 0711.2624, arXiv.org, revised Jun 2008.
  5. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
  6. 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.
  7. �lvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
  8. M. Raberto & E. Scalas & F. Mainardi, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Papers cond-mat/0203596, arXiv.org.
  9. Enrico Scalas, 2006. "Mixtures of compound Poisson processes as models of tick-by-tick financial data," Papers physics/0608217, arXiv.org.
  10. Mark M. Meerschaert & Enrico Scalas, 2006. "Coupled continuous time random walks in finance," Papers physics/0608281, arXiv.org.
  11. Gerald Cheang & Carl Chiarella, 2011. "A Modern View on Merton's Jump-Diffusion Model," Research Paper Series 287, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. 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.
  13. Enrico Scalas, 2011. "A class of CTRWs: Compound fractional Poisson processes," Papers 1103.0647, arXiv.org.
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