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Equivalent Martingale Measure (equivalent + martingale_measure)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	100%

Selected Abstracts

Generic Existence and Robust Nonexistence of Numéraires in Finite Dimensional Securities Markets

MATHEMATICAL FINANCE, Issue 4 2000
Bruno Girotto
A numéraire is a portfolio that, if prices and dividends are denominated in its units, admits an equivalent martingale measure that transforms all gains processes into martingales. We first supply a necessary and sufficient condition for the generic existence of numéraires in a finite dimensional setting. We then characterize the arbitrage-free prices and dividends for which the absence of numéraires survives any small perturbation preserving no arbitrage. Finally, we identify the cases when any small, but otherwise arbitrary, perturbation of prices and dividends preserves either the existence of numéraires, or their nonexistence under no arbitrage. [source]

The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets

MATHEMATICAL FINANCE, Issue 1 2000
Marco Frittelli
Let , be a family of stochastic processes on a given filtered probability space (,, F, (Ft)t,T, P) with T,R+. Under the assumption that the set Me of equivalent martingale measures for , is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to P, in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy. [source]

Alternative tilts for nonparametric option pricing

THE JOURNAL OF FUTURES MARKETS, Issue 10 2010
M. Ryan Haley
This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie,Read family of divergence measures. Alhough the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black,Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:983,1006, 2010 [source]

No Arbitrage in Discrete Time Under Portfolio Constraints

MATHEMATICAL FINANCE, Issue 3 2001
Laurence Carassus
In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997). [source]