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Negative call prices

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Abstract

We show that the existence of an equivalent local martingale measure for asset prices does not prevent negative prices for European calls written on positive stock prices. In particular, we illustrate that many standard no-arbitrage arguments implicitly rely on conditions stronger than the No Free Lunch With Vanishing Risk (NFLVR) assumption. The discrepancy between replicating prices and market prices for a contingent claim may be observed in a model satisfying NFLVR since certain trading strategies of buying one portfolio and selling another one are often excluded by standard admissibility constraints.

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Notes

  1. Negative asset prices can, however, be observed in the market, for instance in the wind energy market. These negative prices occur primarily due to storage costs; see for the example the Bloomberg article Windmill Boom Cuts Electricity Prices in Europe by J. van Loon from April 23, 2010, retrieved from http://www.bloomberg.com/news/2010-04-22/windmill-boom-curbs-electric-power-prices.html. In this paper, we assume a frictionless market, in particular, an agent does not incur costs from holding an asset.

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Acknowledgments

I am grateful to Travis Fisher, Mike Hogan, Ioannis Karatzas, Arseniy Kukanov, Radka Pickova, Philip Protter, Sergio Pulido, Murad Taqqu, and Mike Tehranchi for fruitful discussions on the subject matter of this paper. I thank an anonymous referee for her or his helpful comments. This work was partially supported by the National Science Foundation DMS Grant 09-05754.

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  1. Oxford-Man Institute of Quantitative Finance and Mathematical Institute, University of Oxford, Eagle House, Walton Well Road, Oxford, OX2 6ED, UK

    Johannes Ruf

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Ruf, J. Negative call prices. Ann Finance 9, 787–794 (2013). https://doi.org/10.1007/s10436-012-0221-2

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  • DOI: https://doi.org/10.1007/s10436-012-0221-2

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