106 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
Utility Maximization, Risk Aversion, and Stochastic Dominance
Consider an investor trading dynamically to maximize expected utility from
terminal wealth. Our aim is to study the dependence between her risk aversion
and the distribution of the optimal terminal payoff.
Economic intuition suggests that high risk aversion leads to a rather
concentrated distribution, whereas lower risk aversion results in a higher
average payoff at the expense of a more widespread distribution.
Dybvig and Wang [J. Econ. Theory, 2011, to appear] find that this idea can
indeed be turned into a rigorous mathematical statement in one-period models.
More specifically, they show that lower risk aversion leads to a payoff which
is larger in terms of second order stochastic dominance.
In the present study, we extend their results to (weakly) complete
continuous-time models. We also complement an ad-hoc counterexample of Dybvig
and Wang, by showing that these results are "fragile", in the sense that they
fail in essentially any model, if the latter is perturbed on a set of
arbitrarily small probability. On the other hand, we establish that they hold
for power investors in models with (conditionally) independent increments.Comment: 14 pages, 1 figure, to appear in Mathematics and Financial Economic
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
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