2017/02/23 by Alexander M. G. Cox, Cox, Alexander M. G., Sam M. Kinsley +1
Economics, Econometrics and Finance · Mathematics · #60G40 #91G20 #Capital Investment and Risk Analysis #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G40 #msc:91G20 #q-fin.MF #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1702.07169
arxiv created 2017/02/23 · openalex publication_date 2017/02/23 · arxiv updated 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglböck-Cox-Huesmann. This stopping time can be represented as the hitting time of some region by a Brownian motion, but unlike other solutions of e.g. Root, this region is not unique. Much of this paper is dedicated to characterising the choice of the embedding region that gives the required optimality property. Notably, this appears to be the first solution to the SEP where the solution is not uniquely characterised by its geometric structure, and an additional condition is needed on the stopping region to guarantee that it is the optimiser. An important part of determining the optimal region is identifying the correct form of the dual solution, which has a financial interpretation as a model-independent superhedging strategy.