Related papers: Option Pricing in an Imperfect World
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…
We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging and…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for…
This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price…
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…
Standard rational expectations models with an occasionally binding zero lower bound constraint either admit no solutions (incoherence) or multiple solutions (incompleteness). This paper shows that deviations from full-information rational…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…
Economic models may exhibit incompleteness depending on whether or not they admit certain policy-relevant features such as strategic interaction, self-selection, or state dependence. We develop a novel test of model incompleteness and…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…