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Finite arbitrage times and the volatility smile?

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  • Otto, Matthias

Abstract

Extending previous work on non-equilibrium option pricing theory (Eur. Phys. J. 14 (2000) 383–394), a mean field approach is developed to understand the curvature of (implied by Black–Scholes (BS)) volatility surfaces (curves) as a function of moneyness (strike price divided by price). The previously developed hypothesis of a finite arbitrage time during which fluctuations around the equilibrium state (absence of arbitrage) are allowed to occur is generalized as follows. Instead of a unique arbitrage time independant of moneyness, a distribution of arbitrage times will be assumed, where the mean arbitrage time will be a function of moneyness. This hypothesis is motivated by the fact that the trading volume is the largest for at-the-money options. Assuming now the arbitrage time to be inversely proportional to trading volume naturally leads to our generalized hypothesis on the mean arbitrage time. Consequences on plain vanilla option prices will be studied.

Suggested Citation

  • Otto, Matthias, 2001. "Finite arbitrage times and the volatility smile?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 299-304.
    • Handle: RePEc:eee:phsmap:v:299:y:2001:i:1:p:299-304
    DOI: 10.1016/S0378-4371(01)00309-0
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    References listed on IDEAS

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    1. Kirill Ilinski, 1999. "How to account for virtual arbitrage in the standard derivative pricing," Papers cond-mat/9902047, arXiv.org.
    2. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, September.
    3. David Heath & Eckhard Platen & M. Schweizer, 1998. "Comparison of Some Key Approaches to Hedging in Incomplete Markets," Research Paper Series 1, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. 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.
    2. Chargoy-Corona, Jesús & Ibarra-Valdez, Carlos, 2006. "A note on Black–Scholes implied volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 681-688.

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