Approximate option pricing formula for Barndorff-Nielsen and Shephard model

Local risk-minimization for Barndorff-Nielsen and Shephard models

Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models∗

We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function ap...

Merton’s problem for an investor with a benchmark in a Barndorff-Nielsen and Shephard market

To try to outperform an externally given benchmark with known weights is the most common equity mandate in the financial industry. For quantitative investors, this task is predominantly approached by optimizing their portfolios consecutively over short time horizons with one-period models. We seek in this paper to provide a theoretical justification to this practice when the underlying market i...

Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit estimator based on martingale estimating functions in a bivariate model that is not a diffusion, but ad...

An option pricing formula for the GARCH diffusion model

We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model. Using Monte Carlo simulations, we show that this approximation formula is accurate for a large set of reasonable parameters. Finally, we...