Vol. 13, No. 4, 2020

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Stability and asymptotic analysis of the Föllmer–Schweizer decomposition on a finite probability space

Sarah Boese, Tracy Cui, Samuel Johnston, Gianmarco Molino and Oleksii Mostovyi

Vol. 13 (2020), No. 4, 607–623
Abstract

First, we consider the problem of hedging in complete binomial models. Using the discrete-time Föllmer–Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in incomplete trinomial models, we examine the extension of the sequential regression approach for approximation of contingent claims. Then, on a finite probability space, we investigate stability of the discrete-time Föllmer–Schweizer decomposition with respect to perturbations of the stock price dynamics and, finally, perform its asymptotic analysis under simultaneous perturbations of the drift and volatility of the underlying discounted stock price process, where we prove stability and obtain explicit formulas for the leading-order correction terms.

Keywords
Föllmer–Schweizer decomposition, simultaneous perturbations of the drift and volatility, asymptotic analysis, stability
Mathematical Subject Classification 2010
Primary: 60G07, 93E20, 91G10, 91G20, 90C31
Secondary: 60H30, 93E24
Milestones
Received: 11 January 2020
Accepted: 23 May 2020
Published: 20 November 2020

Communicated by Jonathon Peterson
Authors
Sarah Boese
Vassar College
Poughkeepsie, NY
United States
Tracy Cui
Carnegie Mellon University
Pittsburgh, PA
United States
Samuel Johnston
Willamette University
Salelm, OR
United States
Gianmarco Molino
Department of Mathematics
University of Connecticut
Storrs, CT
United States
Oleksii Mostovyi
Department of Mathematics
University of Connecticut
Storrs, CT
United States