| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 974583 | Physica A: Statistical Mechanics and its Applications | 2015 | 9 Pages |
Abstract
•Mathematical consistency and no-arbitrage in a fractional volatility market model.•Market not complete if the volatility process is independent from the price process.•Market arbitrage free and complete when driven by a unique process.•Arbitrage free complete market displays leverage properties as in empirical data.
When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
R. Vilela Mendes, M.J. Oliveira, A.M. Rodrigues,