Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a non-decreasing Lévy process constitute a useful and very general class of stationary, non-negative continuous-time processes which have been used, in particular, for the modelling of stochastic volatility. Brockwell, Davis and Yang (2011) considered the fitting of CARMA models to closely an...

We study infinite–horizon, optimal switching problems under a general class of stochastic volatility models that exhibit “fast” mean–reversion by using techniques from homogenisation theory. This leads to perturbation theory, providing closed–form approximations to the full switching problem which is often intractable, both analytically and numerically. We apply our general results to certain, ...

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to estimate ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAXmodel. We explore nonlinear departures from these lin...

A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved. The estimator is shown to be also robust to market microstructure noise induced by price discreteness and bid-ask spreads.

We investigate the use of subsampling for conducting inference about quadratic variation of a discretely observed di¤usion process under an in…ll asymptotic scheme. The subsampling method of Politis and Romano (1994) has been shown to be useful in many situations as a way of conducting inference under weak assumptions and without utilizing knowledge of limiting distributions. We show that this ...

We develop a stochastic volatility option pricing model that exploits the informative content of historical high frequency data. Using the Two Scales Realized Volatility as a proxy for the unobservable returns volatility, we propose a simple (affine) but effective long-memory process: the Heterogeneous Auto-Regressive Gamma (HARG) model. This discrete–time process, combined with an exponential ...

Recorded prices are known to diverge from their “efficient” values due to the presence of market microstructure contaminations. The microstructure noise creates a dichotomy in the model-free estimation of integrated volatility. While it is theoretically necessary to sum squared returns that are computed over very small intervals to better indentify the underlying volatility over a period, the s...

I propose a bond-specific, time-varying friction measure of round-trip liquidity costs. The measure is robust to outliers in daily bond returns and accounts for the idiosyncratic information behind bond trading decisions. Using transactions from January 2004 to December 2010, I find that liquidity costs display a strong correlation with credit conditions and peaked during the sub-prime crisis. ...

This paper constructs estimates of daily stock index volatilities and correlation using high-frequency (one-minute) intraday stock indices. The key feature of these ‘realized’ volatilities and correlations is that they are not only model-free but also approximately measurement-error-free. In fact, they can be treated as observed rather than latent, so that direct modeling and forecasting of the...