Speaker
Description
For modelling portfolios of risky securities, practitioners need multi-asset pricing models that meet several requirements. On the one hand, the model should be flexible enough to capture a variety of regimes useful for pricing assets across different markets. On the other hand, it should be calibratable to empirical data and allow sampling from the exact distribution without introducing approximation bias. The pool of such solvable stochastic models is limited and is mainly based on multivariate Brownian motion with or without stochastic-time subordination [1]. Another common approach is the copula method, in which the multivariate distribution is obtained by combining a multivariate uniform distribution function defined on a unit hypercube with marginal distribution functions [2]. However, its main limitation is that it requires computing inverse distribution functions, which can be computationally challenging for advanced models.
In this talk, we present a multi-asset diffusion process in which the marginal distributions follow the constant elasticity of variance (CEV) diffusion model. Our approach expresses the CEV process in terms of a randomized gamma random variable [3]. We apply the copula method to sample dependent gamma random variables, then construct the multi-asset CEV process by combining them with nonlinear mappings and Poisson randomizers. This approach preserves the marginal distributions and allows us to compute correlations between asset values. For calibration, we first estimate the parameters of each marginal process using maximum likelihood estimation (MLE) or least squares. We then transform the empirical data and estimate the correlations between asset values. The dependency parameters are computed by matching the theoretical and empirical correlations.
[1] Bianchi, M. L., A. Hitaj, and G. L. Tassinari. “A Welcome to the Jungle of Continuous-Time Multivariate Non-Gaussian Models Based on Lévy Processes Applied to Finance.” Ann. Oper. Res. 352(3): 859–900 (2025)
[2] Cherubini, U., E. Luciano, and W. Vecchiato. Copula Methods in Finance. Wiley, 2004
[3] Makarov, R. N., and D. Glew. “Exact Simulation of Bessel Diffusions.” Monte Carlo Methods Appl. 16(3–4) (2010)
