This paper proposes a stochastic volatility model (PAR-SV ) in which the log-volatility follows a …rst-order periodic autoregression. This model aims at representing time series with volatility displaying a stochastic periodic dynamic structure, and may then be seen as an alternative to the familiar periodic GARCH process. The probabilistic structure of the proposed PAR-SV model such as periodi...

This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochas...

This paper studies the empirical performance of jump-di usion models that allow for stochastic volatility and correlated jumps a ecting both prices and volatility. We propose a simulation method for conducting likelihood based inference from a panel of options data, as well as returns data simultaneously. Empirical results from S&P 500 returns/options di er from the current literature in severa...

A passport option is a call option on the profits of a trading account. In this article we investigate the robustness of passport option pricing by incorporating stochastic volatility. The key feature of a passport option is the holders’ optimal strategy. It is known that in the case of exponential Brownian motion the strategy is to be long if the trading account is below zero and short if the ...

We develop a new framework to calibrate stochastic volatility option pricing models to an arbitrary prescribed set of prices of liquidly traded options. Our approach produces an arbitrage-free stochastic volatility di usion process that minimizes the distance to a prior di usion model. We use the notion of relative entropy (also known under the name of Kullback-Leibler distance) to quantify the...

This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models in Benhamou et al. (2009c) for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurat...

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model’s parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on t...