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...

Default dependency structure is crucial in pricing multi-name credit derivatives as well as in credit risk management. In this paper, we extend the first passage model for one name with stochastic volatility (Fouque-Sircar-Sølna, Applied Mathematical Finance 2006) to the multi-name case. Correlation of defaults is generated by correlation between the Brownian motions driving the individual name...

This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal a...

The availability of intra-day data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets, called realised volatility, to study the stochastic properties of returns. Here we provide a statistical basis for realised volatility and show how it can be used to estimate the parameters of stochastic volatility models. Models covere...

In this paper we present a strategy to form a class of control variates for pricing Asian options under the stochastic volatility models by the risk-neutral pricing formula. Our idea is employing a deterministic volatility function σ(t) to replace the stochastic volatility σt. Under the Hull and White model[11] and the Heston model[10], the deterministic volatility function σ(t) can be chosen w...

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein-Uhlenbeck and other continous-time CARMA models as well as continous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functi...

Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We ad...