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Asymptotic arbitrage in the Heston model

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  • Fatma Haba
  • Antoine Jacquier

Abstract

In the context of the Heston model, we establish a precise link between the set of equivalent martingale measures, the ergodicity of the underlying variance process and the concept of asymptotic arbitrage proposed in Kabanov-Kramkov and in Follmer-Schachermayer.

Suggested Citation

  • Fatma Haba & Antoine Jacquier, 2013. "Asymptotic arbitrage in the Heston model," Papers 1302.6491, arXiv.org, revised Apr 2014.
  • Handle: RePEc:arx:papers:1302.6491
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    References listed on IDEAS

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    1. Martin Mbele Bidima & Miklos Rasonyi, 2012. "On long-term arbitrage opportunities in Markovian models of financial markets," Annals of Operations Research, Springer, vol. 200(1), pages 131-146, November.
    2. repec:dau:papers:123456789/10555 is not listed on IDEAS
    3. Irene Klein & Emmanuel LĂ©pinette & Lavinia Perez-Ostafe, 2014. "Asymptotic arbitrage with small transaction costs," Finance and Stochastics, Springer, vol. 18(4), pages 917-939, October.
    4. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    5. 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..
    6. Dmitry Rokhlin, 2008. "Asymptotic arbitrage and numéraire portfolios in large financial markets," Finance and Stochastics, Springer, vol. 12(2), pages 173-194, April.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11.
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