The behavior of the implied volatility surface for European options was analysed in detail by Zumbach and Fernandez for prices computed with a new option pricing scheme based on the construction of the risk-neutral measure for realistic processes with a finite time increment. The resulting...

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread,...

This paper presents a complete computation of option prices based on a realistic process for the underlying and on the construction of a risk-neutral measure as induced by a no-arbitrage replication strategy. The underlying is modelled with a long-memory ARCH process, with relative returns,...

For a given time horizon DT, this article explores the relationship between the realized volatility (the volatility that will occur between t and t+DT), the implied volatility (corresponding to at-the-money option with expiry at t+DT), and several forecasts for the volatility build from...

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance...

The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are...

Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in the next time period is a measure of the response...

This paper investigates the scaling dependencies between measures of 'activity' and of 'size' for companies included in the FTSE 100. The 'size' of companies is measured by the total market capitalization. The 'activity' is measured with several quantities related to trades (transaction value...

We introduce a new family of processes that include the long memory (LM) (power law) in the volatility correlation. This is achieved by measuring the historical volatilities on a set of increasing time horizons and by computing the resulting effective volatility by a sum with power law weights....

The long memory linear ARCH process is extended to a multivariate universe, where the natural cross-product structure of the covariance is generalized by adding two bi-linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data and...