Speaker: Thomas Kirkegaard Kloster (Aarhus University)
Title: Expanding on orthogonal expansions for option pricing
Abstract: In this talk we consider the problem of approximating prices of financial derivatives, such as options, by means of orthogonal density expansions. We focus on option pricing models in which standard methods are slow or infeasible, thus necessitating alternative perspectives. We recap the classical theory of density expansions and their uses in this context and argue that the crucial ingredient in making such expansions operational is the so-called reference density. Typically, the reference density must be explicitly known, but we show how to expand the pool of potential reference densities considerably. More precisely, by employing standard transform inversion techniques, we broaden the pool of reference densities to include densities that are only known up to their characteristic function. This ultimately yields simple price expansions in terms of modified payoffs under a simpler pricing model – the reference model – and we illustrate how to select this reference model in practice, to provide good approximations at very low expansion orders in stochastic volatility models based on affine jump diffusions and rough volatility.
The talk is based on joint work with Elisa Nicolato.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.