Semimartingale probabilistic setups lead to very useful volatility estimation. The integrated volatility can be consistently estimated by the realized one according to the quadratic variation principle, even if the convergence speed can result relatively slow, depending on noise and market...

The aim of this work is to take into account the effects of long memory in volatility on derivative hedging. This idea is an extension of the work by Fedotov and Tan [Stochastic long memory process in option pricing, Int. J. Theor. Appl. Finance 8 (2005) 381–392] where they incorporate...

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless...

In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under...

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to...

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker–Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination...

Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993)  [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation...

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these...

We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Drăgulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982–1999, we find a very good...

The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage effect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility...