We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an ...

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 constant volatility models up to stochastic volatility. We also survey less commonly known models e.g. hybrid models. We explain various volatility types (e....

We provide a formulation of stochastic volatility based on Gaussian processes, a flexible framework for Bayesian nonlinear regression. The advantage of using Gaussian processes in this context is to place volatility forecastingwithin a regression framework; this allows a large number of explanatory variables to be used for forecasting, a task difficult with standard volatility-forecasting formu...

Some relationships between ARCH-type and Stochastic Volatility models are investigated. New model formulations are derived through a transformation of a GARCH-M process and the name Generalized Bilinear Stochastic Volatility is suggested. Markovian-type representations are presented and estimation algorithms are proposed.

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff functions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean re...

In this paper we investigate to what extent the bootstrap can be applied conditional mean models, such as regression or time series when volatility of innovations is random and possibly non-stationary. fact, many economic financial displays persistent changes possible non-stationarity. However, theory for models has focused on deterministic unconditional variance little known about performance ...