Related papers: Volatility Decomposition and Estimation in Time-Ch…
We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
We derive the short-maturity asymptotics for prices of options on realized variance in local-stochastic volatility models. We consider separately the short-maturity asymptotics for out-of-the-money and in-the-money options cases. The…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
Implied volatilities form a well-known structure of smile or surface which accommodates the Bachelier model and observed market prices of interest rate options. For the swaptions that we study, three parameters are taken into account for…
The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among…
Modelling financial time series as a time change of a simpler process has been proposed in various forms over the years. One of such recent approaches is called volatility homogenisation decomposition, and has been designed specifically to…
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities.…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is…
We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier type deconvolution kernel density…
We propose a stochastic volatility model for time series of curves. It is motivated by dynamics of intraday price curves that exhibit both between days dependence and intraday price evolution. The curves are suitably normalized to…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely…
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous…
The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…
High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems…
We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic…