Financial markets with volatility uncertainty

By Joerg Vorbrink. 2010

104 citations recorded by the source corpus.

We investigate financial markets under model risk caused by uncertain volatilities. To this end, we consider a financial market that features volatility uncertainty. We use the notion of G-expectation and its corresponding G-Brownian motion recently introduced by Peng (2007) to ensure a mathematically consistent framework. Our financial market consists of a riskless asset and a risky stock with price process modeled by geometric G-Brownian motion. We adapt the notion of arbitrage to this more complex situation, and consider stock price dynamics which exclude arbitrage opportunities. Volatility uncertainty results in an incomplete market. We establish the interval of no-arbitrage prices for general European contingent claims, and deduce explicit results in the Markovian case.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/cd2624c376abd6e05586a05e7d6b3d69ef1892e6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Daniel Fernholz
2. Ioannis Karatzas
3. Soumik Pal
4. Marcel Nutz
5. Mykhaylo Shkolnikov
6. Constantinos Kardaras
7. Tomoyuki Ichiba
8. Gordan Zitkovic

In Management Science and Operations Research

1. Ioannis Karatzas
2. Daniel Fernholz
3. Marcel Nutz
4. Gordan Zitkovic
5. Constantinos Kardaras

Citations in the corpus

• Optimal arbitrage under model uncertainty. (2011, background): “ Similar in this spirit is the strand of work by Shige Peng and his collaborators, surveyed in Peng (2010), regarding the so-called “G-Brownian motion” which exhibits volatility uncertainty [see also Vorbrink (2010), as well as Nutz (2010) for extensions to settings where the range of uncertainty is”