94 research outputs found
Arbitrage and deflators in illiquid markets
This paper presents a stochastic model for discrete-time trading in financial
markets where trading costs are given by convex cost functions and portfolios
are constrained by convex sets. The model does not assume the existence of a
cash account/numeraire. In addition to classical frictionless markets and
markets with transaction costs or bid-ask spreads, our framework covers markets
with nonlinear illiquidity effects for large instantaneous trades. In the
presence of nonlinearities, the classical notion of arbitrage turns out to have
two equally meaningful generalizations, a marginal and a scalable one. We study
their relations to state price deflators by analyzing two auxiliary market
models describing the local and global behavior of the cost functions and
constraints
Superhedging in illiquid markets
We study contingent claims in a discrete-time market model where trading
costs are given by convex functions and portfolios are constrained by convex
sets. In addition to classical frictionless markets and markets with
transaction costs or bid-ask spreads, our framework covers markets with
nonlinear illiquidity effects for large instantaneous trades. We derive dual
characterizations of superhedging conditions for contingent claim processes in
a market without a cash account. The characterizations are given in terms of
stochastic discount factors that correspond to martingale densities in a market
with a cash account. The dual representations are valid under a topological
condition and a weak consistency condition reminiscent of the ``law of one
price'', both of which are implied by the no arbitrage condition in the case of
classical perfectly liquid market models. We give alternative sufficient
conditions that apply to market models with nonlinear cost functions and
portfolio constraints
Stability of the utility maximization problem with random endowment in incomplete markets
We perform a stability analysis for the utility maximization problem in a
general semimartingale model where both liquid and illiquid assets (random
endowments) are present. Small misspecifications of preferences (as modeled via
expected utility), as well as views of the world or the market model (as
modeled via subjective probabilities) are considered. Simple sufficient
conditions are given for the problem to be well-posed, in the sense the optimal
wealth and the marginal utility-based prices are continuous functionals of
preferences and probabilistic views.Comment: 21 pages, revised version. To appear in "Mathematical Finance"
Hedging, arbitrage and optimality with superlinear frictions
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g
processes, this paper characterizes superhedging prices, absence of arbitrage,
and utility maximizing strategies, under general frictions that make execution
prices arbitrarily unfavorable for high trading intensity. Such frictions
induce a duality between feasible trading strategies and shadow execution
prices with a martingale measure. Utility maximizing strategies exist even if
arbitrage is present, because it is not scalable at will.Comment: Published at http://dx.doi.org/10.1214/14-AAP1043 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
No free lunch for markets with multiple num\'eraires
We consider a global market constituted by several submarkets, each with its
own assets and num\'eraire. We provide theoretical foundations for the
existence of equivalent martingale measures and results on superreplication
prices which allows to take into account difference of features between
submarkets
Valuation and parities for exchange options
Valuation and parity formulas for both European-style and American-style
exchange options are presented in a general financial model allowing for jumps,
possibility of default and "bubbles" in asset prices. The formulas are given
via expectations of auxiliary probabilities using the change-of-numeraire
technique. Extensive discussion is provided regarding the way that folklore
results such as Merton's no-early-exercise theorem and traditional parity
relations have to be altered in this more versatile framework.Comment: 19 page
Reduced form modeling of limit order markets
This paper proposes a parametric approach for stochastic modeling of limit
order markets. The models are obtained by augmenting classical perfectly liquid
market models by few additional risk factors that describe liquidity properties
of the order book. The resulting models are easy to calibrate and to analyze
using standard techniques for multivariate stochastic processes. Despite their
simplicity, the models are able to capture several properties that have been
found in microstructural analysis of limit order markets. Calibration of a
continuous-time three-factor model to Copenhagen Stock Exchange data exhibits
e.g.\ mean reversion in liquidity as well as the so called crowding out effect
which influences subsequent mid-price moves. Our dynamic models are well suited
also for analyzing market resiliency after liquidity shocks
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