A Stochastic Control Approach to No-Arbitrage Bounds Given Marginals, with an Application to Lookback Options
25 Pages Posted: 22 Sep 2011 Last revised: 20 Feb 2013
Date Written: February 2013
Abstract
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows to recover previously known results about Lookback options. In particular, our methodology induces a new presentation of the Azema-Yor solution of the SEP.
Keywords: Optimal control, volatility uncertainty, convex duality
JEL Classification: C00, G00
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Model-Independent Bounds for Option Prices: A Mass Transport Approach
By Mathias Beiglböck, Pierre Henry-labordere, ...
-
Robust Hedging with Proportional Transaction Costs
By Yan Dolinsky and Halil Mete Soner
-
Martingale Optimal Transport and Robust Hedging in Continuous Time
By Yan Dolinsky and Halil Mete Soner