Dependence calibration and portfolio fit with factor-based subordinators

Abstract

The paper explores the properties of a class of multivariate Lévy processes, used for asset returns, with a focus on describing in an economic sensible and empirically appropriate way both linear and nonlinear dependence. The processes are subordinated Brownian motions. The subordinator has a common and an idiosyncratic component, to reflect the properties of trade, which it represents. A calibration to a portfolio of ten US stock indices returns over the period 2009-2013 shows that the hyperbolic specification fits very well marginal distributions, the overall correlation matrix and the return distribution of both long-only and long-short random portfolios, which incorporate also nonlinear dependence. Their tail behavior is well captured also by the variance gamma specification. The main message is not only the goodness of fit, but also the flexibility in capturing dependence and the easiness of calibration on large sets of returns.

Multivariate Factor-Based Processes With Sato Margins

“…The correlation flexibility of these models has been studied in the historical setting by Luciano et al (2016) and in the risk neutral one by Marena et al (2015). In both cases they provide an overall good performance.…”

“…These classes of models have two di↵erent sets of parameters: idiosyncratic parameters, i.e., stock-specific, and common ones. Marginal distributions do not depend on common parameters, which are usually used to fit the correlation structure, see, e.g., Luciano and Semeraro (2010), Guillaume (2012) and Luciano et al (2016). This structure allows us to perform a satisfactory calibration of the marginal processes and, for given pairs of marginal parameters, to compare the correlation range allowed by the ⇢↵-Sato process with the correlation range allowed by their Lévy counterpart.…”

Option pricing in time-changed Lévy models with compound Poisson jumps

“…Luciano and Schoutens [27] modeled the S&P500, the Nikkei225 and the Eurostoxx50 financial indexes by the variancegamma process. Luciano et al [29] and Wallmeier and Diethelm [43] confirmed the using of variance-gamma distribution for the modeling of the US and the Swiss stock markets, respectively.…”

“…The result of Theorem 1 follows from (34), where the functions DC(n 1 , n 2 , n 3 ) are computed with respect to (30) using (7) and (32) where I is defined in (29) and computed by (32)…”

A Credit-Risk Valuation under the Variance-Gamma Asset Return

“…Among others, let us mention the papers by Daal and Madan (2005), Finlay and Seneta (2006), Linders and Stassen (2016), Luciano et al (2016), Luciano and Schoutens (2006), Moosbrucker (2006), Mozumder et al (2015), Rathgeber et al (2016), and Wallmeier and Diethelm (2012), where the variance-gamma distribution is confirmed as a very good model to make out the statistics. For approximations of processes by the variance-gamma one, see Eichelsbacher and Thäle (2015).…”