We consider general regime switching stochastic volatility models where both the asset and the volatility dynamics depend on the values of a Markov jump process. Due to the stochastic volatility and the Markov regime switching, this financial market is thus incomplete and perfect pricing and hedging of options are not possible. Thus, we are interested in finding formulae to solve the problem of...

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. M...

This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jumpamplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlimited borro...

Abstract This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jump-amplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlim...

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein-Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous ...

Particle filters are an important class of online posterior density estimation algorithms. In this paper we propose a real coded genetic algorithm particle filter (RGAPF) for the dual estimation of stochastic volatility and parameters of a Heston type stochastic volatility model. We compare the performance of our hybrid particle filter with a parameter learning particle filter present in litera...

We consider Taylor’s stochastic volatility model when the innovations of the hidden log-volatility process have a Laplace distribution (`1 exponential density), rather than the standard Gaussian distribution (`2) usually employed. Using a distribution with heavier tails allows better modeling of the abrupt changes of regime observed in financial time series. We derive here the moments and autoc...

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast sca...

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian prior works allow this approach to provide parsimonious skew structure and...