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National Repository of Grey Literature 1 records found  Search took 0.01 seconds. 
Continuous market models with stochastic volatility
 Petrovič, Martin ; Maslowski, Bohdan (advisor) ; Hlubinka, Daniel (referee)
Vilela Mendes et al. (2015), based on the discovery of long-range dependence in the volatility of stock returns, proposed a stochastic volatility continuous mar- ket model where the volatility is given as a transform of the fractional Brownian motion (fBm) and studied its No-Arbitrage and completeness properties under va- rious assumptions. We investigate the possibility of generalization of their results from fBm to a wider class of Hermite processes. We have reworked and completed the proofs of the propositions in the cited article. Under the assumption of indepen- dence of the stock price and volatility driving processes the model is arbitrage-free. However, apart from a case of a special relation between the drift and the volatility, the model is proved to be incomplete. Under a different assumption that there is only one source of randomness in the model and the volatility driving process is bounded, the model is arbitrage-free and complete. All the above results apply to any Hermite process driving the volatility. 1
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