"Leverage, heavy-tails and correlated jumps in stochastic volatility models"

This paper proposes the efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps. We illustrate our method using simulated data and analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model.

Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Levy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements, but the maximally allowable premium on downward index movements.dampened power law; alpha-stable distribution; central limit theorem; upside movement; downside movement

"Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models"

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.

Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailness as well as leverage effects. An efficient Markov chain Monte Carlo estimation method is described exploiting a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as a mixing distribution. The proposed method is illustrated using simulated data, daily TOPIX and S&P500 stock returns. The model comparison for stock returns is conducted based on the marginal likelihood in the empirical study. The strong evidence of the leverage and asymmetric heavy-tailness is found in the stock returns. Further, the prior sensitivity analysis is conducted to investigate whether obtained results are robust with respect to the choice of the priors.generalized hyperbolic skew Student's t-distribution, Markov chain Monte Carlo, Mixing distribution, State space model, Stochastic volatility, Stock returns

The effect of non-ideal market conditions on option pricing

Option pricing is mainly based on ideal market conditions which are well represented by the Geometric Brownian Motion (GBM) as market model. We study the effect of non-ideal market conditions on the price of the option. We focus our attention on two crucial aspects appearing in real markets: The influence of heavy tails and the effect of colored noise. We will see that both effects have opposite consequences on option pricing.Comment: 26 pages and 8 colored figures. Invited Talk in "Horizons in complex systems", Messina, 5-8 December 2001. To appear in Physica-

Scaling and multiscaling in financial series: a simple model

We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments. Despite its few parameters, the model is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with a remarkable accuracy.Comment: 32 pages, 5 figures. Substantial revision, following the referee's suggestions. Version to appear in Adv. in Appl. Proba