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Displaying similar documents to “Bounds for the range of American contingent claim prices in the jump-diffusion model”

Arbitrage in a simple model with general transaction costs

Jakub Olejnik (2005)

Applicationes Mathematicae

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We study a version of no arbitrage condition in a simple model with general transaction costs. Our condition is equivalent to the existence of an equivalent martingale measure.

Discrete-time market models from the small investor point of view and the first fundamental-type theorem

Marek Karaś, Anna Serwatka (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we...

The martingale method of shortfall risk minimization in a discrete time market

Marek Andrzej Kociński (2012)

Applicationes Mathematicae

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The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.

Refined wing asymptotics for the Merton and Kou jump diffusion models

Stefan Gerhold, Johannes F. Morgenbesser, Axel Zrunek (2015)

Banach Center Publications

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Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features an interesting "almost power law" tail.

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

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A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving...

Incompleteness of the bond market with Lévy noise under the physical measure

Michał Barski (2015)

Banach Center Publications

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The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.