Financial markets with volatility uncertainty
AbstractWe 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.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 441.
Length: 40 pages
Date of creation: Nov 2010
Date of revision:
Pricing of contingent claims; incomplete markets; volatility uncertainty; G–Brownian motion stochastic calculus;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-18 (All new papers)
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- Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
- Larry G. Epstein & Shaolin Ji, 2012.
"Ambiguous Volatility and Asset Pricing in Continuous Time,"
CIRANO Working Papers, CIRANO
- Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
- Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous volatility and asset pricing in continuous time," Papers 1301.4614, arXiv.org.
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