Explicit Representation of Cost-Efficient Strategies - 15 décembre 2014

Carole BERNARD, Phelim P. BOYLE, Steven VANDUFFEL

In this paper, we give an explicit representation of the lowest cost strategy to achieve a given payoff distribution (that we call “cost-efficient” strategy). For any inefficient strategy, we are able to construct financial derivatives which dominate in the sense of first-order or second-order stochastic dominance. We highlight the connections between cost-efficiency and dependence. This allows us to extend the theory to deal with state-dependent constraints to better reflect real-world preferences. We show in particular that path-dependent strategies (although inefficient in the Black Scholes setting) may become optimal in the presence of state-dependent constraints.

Stock Returns Memories: a “Stardust” Memory? - 15 décembre 2014

Julien FOUQUAU, Philippe SPIESER

This article aims at investigating econometrically the market efficiency concept through an analysis of the dependence structure of stock market index returns. To that purpose, we use a large range of methods in this paper. Six different estimation procedures are applied to obtain the Hurst exponent, starting with the “R/S” approach, continuing with ARFIMA models and ending with wavelet models. We investigate the possible presence of long or short-memory in twelve market indexes between three periods, namely (1960-2013), (1980-2013) and (1990-2013). Our conclusions depend on the degree of financial maturity: most emerging markets display the presence of memory, whereas mature markets show an absence of or very short-memory dynamics.

The Computation of Risk Budgets under the Lévy Process Assumption - 15 décembre 2014

Olivier LE COURTOIS, Christian WALTER

This paper revisits the computation of Value-at-Risk and other risk indicators based on the use of Lévy processes. We first provide a new presentation of Variance Gamma Processes with Drift: we reconstruct them in an original way, starting from the exponential distribution. Then, we derive general Fourier formulas that allow us to compute VaR quickly and efficiently, but also other typical indicators like Tail Conditional Expectation (TCE). Based on such a formula, we conduct a study of the term structure of VaR, and provide a discussion of the Basle 2 and Solvency II agreements.