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On volatility smile and an investment strategy with out-of-the-money calls

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  • Jarno Talponen

Abstract

A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The main points of this note are the following. First, the presented trading strategy appears very lucrative in the Black-Scholes-Merton (BSM) framework. In fact, it is such even to the extent that the BSM model turns out to be, in a sense, incompatible with the CAPM. Second, if one wishes to adapt these models together, then the adjustment of the consistent pricing rule (i.e. modifying state price densities) inevitably leads to some form of volatility smile and this is the main point of the paper. Moreover, these observations arise from purely structural considerations.

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  • Jarno Talponen, 2014. "On volatility smile and an investment strategy with out-of-the-money calls," Papers 1410.1426, arXiv.org.
    • Handle: RePEc:arx:papers:1410.1426
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    References listed on IDEAS

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
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    3. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 259-275, September.
    4. repec:dgr:rugsom:00e08 is not listed on IDEAS
    5. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65.
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