MCFAM Seminar - The asymptotic expansion of the regular discretization error of Itô integrals

Speaker: Elisa Alòs

Abstract: In this talk, we present an Edgeworth-type refinement of the central limit theorem for the discretization error of Itô integrals. Toward this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula. Two applications to finance are given: the asymptotic of discrete hedging error under the Black-Scholes model and the difference between continuously and discretely monitored variance swap payoffs under stochastic volatility models. Both of these applications shed light on hedging errors usually neglected in the continuous-time framework of mathematical finance. A short introduction to the anticipating Itô's calculus is given at the beginning of the talk. (Joint work with Masaaki Fukasawa).