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Financial markets with volatility uncertainty

Author

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  • Vorbrink, Jörg

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of G–expectation and its corresponding G–Brownian motion recently introduced by Peng (2007). Our financial market consists of a riskless asset and a risky stock with price process modeled by a geometric G–Brownian motion. We adapt the notion of arbitrage to this more complex situation and consider stock price dynamics which exclude arbitrage opportunities. Due to volatility uncertainty the market is not complete any more. We establish the interval of no–arbitrage prices for general European contingent claims and deduce explicit results in a Markovian setting.

Suggested Citation

  • Vorbrink, Jörg, 2017. "Financial markets with volatility uncertainty," Center for Mathematical Economics Working Papers 441, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:441
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    File URL: https://pub.uni-bielefeld.de/download/2909310/2909311
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    Citations

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    Cited by:

    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
    3. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    4. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.

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