Browsing by Author "Mendes, Rui Vilela"
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- A data-reconstructed fractional volatility modelPublication . Mendes, Rui Vilela; Oliveira, Maria JoãoBased on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes and a new option pricing formula are also obtained.
- Fractional boson gas and fractional poisson measure in infinite dimensionsPublication . Oliveira, Maria João; Mendes, Rui VilelaAs a consequence of Haag’s theorem, to obtain a non-trivial theory, one either works with a non-Fock representation or with a Fock representation in a finite volume. Calculations in the Fock representation taking the N,V→ ∞limit with the ratio N/V=ρ fixed, show the equivalence of the free Boson gas and the infinite-dimensional Poisson measure. The N/V limit provides a way to deal with non-trivial infinite systems using the Fock representation. However, by the very nature of the fixed ρ density limit, it is unable to deal with systems with density fluctuations, a shortcoming that is solved by the use of reducible functionals. A particularly interesting reducible functional is the one associated to the infinite-dimensional fractional Poisson measure which we recall in this work.
- The fractional volatility model : no-arbitrage, leverage and completenessPublication . Mendes, Rui Vilela; Oliveira, Maria João; Rodrigues, A. M.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.