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Dynamic option pricing with endogenous stochastic arbitrage

Listed author(s):
  • Contreras, Mauricio
  • Montalva, Rodrigo
  • Pellicer, Rely
  • Villena, Marcelo

Only few efforts have been made in order to relax one of the key assumptions of the Black–Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B–S model to that new trajectory even when the arbitrage already started.

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File URL: http://www.sciencedirect.com/science/article/pii/S0378437110003572
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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 389 (2010)
Issue (Month): 17 ()
Pages: 3552-3564

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Handle: RePEc:eee:phsmap:v:389:y:2010:i:17:p:3552-3564
DOI: 10.1016/j.physa.2010.04.019
Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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  1. Adrian, Tobias, 2009. "Inference, arbitrage, and asset price volatility," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 49-64, January.
  2. Attari, Mukarram & Mello, Antonio S., 2006. "Financially constrained arbitrage in illiquid markets," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2793-2822, December.
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  8. Panayides, Stephanos, 2006. "Arbitrage opportunities and their implications to derivative hedging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 289-296.
  9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  10. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
  11. Figlewski, Stephen, 1984. " Hedging Performance and Basis Risk in Stock Index Futures," Journal of Finance, American Finance Association, vol. 39(3), pages 657-669, July.
  12. Fedotov, Sergei & Panayides, Stephanos, 2005. "Stochastic arbitrage return and its implication for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 207-217.
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