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...

The success of the Black-Scholes (BS) formula is mainly due to the possibility of synthesizing option prices through a unique parameter, the implied volatility, which is so crucial for traders to be directly quoted in many financial markets. This is because the BS formula allows one to immediately convert a volatility into the price at which the related option can be exchanged. The BS model, ho...

Central banks and other forecasters are increasingly interested in various aspects of density forecasts. However, recent sharp changes in macroeconomic volatility – such as the Great Moderation and the more recent sharp rise in volatility associated with greater variation in energy prices and the deep global recession – pose significant challenges to density forecasting. Accordingly, this paper...

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the ...

We study the effect of introducing stochastic volatility in the first passage structural approach to default risk. We analyze the impact of volatility time scales on the yield spread curve. In particular we show that the presence of a short time scale in the volatility raises the yield spreads at short maturities. We argue that combining first passage default modeling with multiscale stochastic...