FS Poseidon POS380 : Cruise Summary Report

20.03.2009 - 06.04.2009 Fort de France, Martinique (France) - Ponta Delgada, Acores (Portugal

Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging

We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas, and volgas of the non-traded and the liquidly traded options.Comment: 44 pages; forthcoming in 'Finance and Stochastics

High-Resilience Limits of Block-Shaped Order Books

We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding problem in an Almgren/Chriss setup with small quadratic trading costs.Comment: 12 page

Option Pricing and Hedging with Small Transaction Costs

An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.Comment: 20 pages, to appear in "Mathematical Finance

Portfolio Choice with Stochastic Investment Opportunities: a User's Guide

This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by means of convex duality. Special emphasis is placed on long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure