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...

The paper introduces the structure of parsimonious Portfolio Single Index (PSI) multivariate conditional and stochastic constant correlation volatility models, and methods for estimation of the underlying parameters. These multivariate estimates of volatility can be used for more accurate portfolio and risk management, to enable efficient forecasting of Value-at-Risk (VaR) thresholds, and to de...

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in ...

Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for time-discretization and Monte Carlo simulation of Heston-type stochastic volatility models. The algorithms are...

Optimal as well as recursive parameter estimation for semimartingales had been studied in Thavaneswaran and Thompson [1, 2]. Recently, there has been a growing interest in modeling volatility of the observed process by nonlinear stochastic processes (Taylor [3]). In this paper, we study the recursive estimates for various classes of discretely sampled continuous time stochastic volatility model...