A Markov chain with an expanding non-uniform grid matching risk-neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with pre-specified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...

Dilip B Madan discusses how even good financial models often fail to perform when applied to real economic data. To overcome market volatility, he suggests, the right model must successfully reduce dimension.

We consider a simple single period economy in which agents invest so as to maximize expected utility of terminal wealth. We assume the existence of three asset classes, namely a riskless asset (the bond), a single risky asset (the stock), and European options of all strikes (derivatives). In...

We discuss a Levy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian...

In this paper we investigate alternative Levy base correlation models that arise from the Gamma, Inverse Gaussian and CMY distribution classes. We compare these models with the basic (exponential) Levy base correlation model and the classical Gaussian base correlation model. For all investigated...

<title>Abstract</title> This paper provides a new market implied calibration based on a moment matching methodology where the moments of the risk-neutral density function are inferred from at-the-money and out-the-money European vanilla option quotes. In particular, we derive a model-independent risk-neutral...

In this paper we discuss moment swaps. These derivatives depend on the realized higher moments of the underlying. A special case is the nowadays popular variance swaps. After introducing moment swaps we discuss how to hedge these derivatives. Moreover, we show how the classical hedge of the...

We define the class of local Levy processes. These are Levy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...

This paper follows the insights of Black and Scholes (1973 J. Political Economy 81 637-54) and Merton (1973 Bell J. Economics Management Sci. 4 141-83) in contexts where their conclusions cannot be exactly obtained. Specifically, we consider an infinite activity Levy process with no continuous...