Financial markets with volatility uncertainty

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 441

Classification and Topics

• Classification: Wirtschaft ; Contingent Pricing; Futures Pricing; option pricing ; Criteria for Decision-Making under Risk and Uncertainty ; Optimization Techniques; Programming Models; Dynamic Analysis
• Subject: pricing of contingent claims ; incomplete markets ; volatility uncertainty ; G-Brownian motion stochastic calculus ; Optionspreistheorie ; Finanzmarkt ; Unvollkommener Markt ; Börsenkurs ; Volatilität ; Stochastischer Prozess ; Theorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Vorbrink, Jörg
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/43819
• Last update: 10.03.2025, 11:45 AM CET