Financial markets with volatility uncertainty

Jörg Vorbrink
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Jörg Vorbrink: Center for Mathematical Economics, Bielefeld University

No 441, Center for Mathematical Economics Working Papers from 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.

Keywords: Pricing of contingent claims; incomplete markets; volatility uncertainty; G–Brownian motion stochastic calculus (search for similar items in EconPapers)
Date: 2017-03-20
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:441

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