211 research outputs found
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
On using shadow prices in portfolio optimization with transaction costs
In frictionless markets, utility maximization problems are typically solved
either by stochastic control or by martingale methods. Beginning with the
seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713],
stochastic control theory has also been used to solve various problems of this
type in the presence of proportional transaction costs. Martingale methods, on
the other hand, have so far only been used to derive general structural
results. These apply the duality theory for frictionless markets typically to a
fictitious shadow price process lying within the bid-ask bounds of the real
price process. In this paper, we show that this dual approach can actually be
used for both deriving a candidate solution and verification in Merton's
problem with logarithmic utility and proportional transaction costs. In
particular, we determine the shadow price process.Comment: Published in at http://dx.doi.org/10.1214/09-AAP648 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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