Option spanning beyond $$L_p$$ L p -models

Gao, Niushan; Xanthos, Foivos

doi:10.1007/s11579-017-0185-0

Math Finan Econ

2017

DOI: 10.1007/s11579-017-0185-0

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Option spanning beyond $$L_p$$ L p -models

Niushan Gao

Foivos Xanthos

Abstract: The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the results in [13,14,24] for L p -models. We also apply the spanning power properties to the pricing problem. In particular, we show that prices on call and put options of a limited liability asset can be uniquely extended by arbitrage to all marketed contingent claims written on the asset.Date: July 17, 2018. 2010 Mathematics Subject Classification. Pri… Show more

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Cited by 5 publications

References 36 publications

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Fundamental theorem of asset pricing with acceptable risk in markets with frictions

Arduca

Munari

2023

Finance Stoch

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We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given market. Trading is subject to nonproportional transaction costs and portfolio constraints, and full replication by way of market instruments is not always possible. Rationality is defined in terms of consistency with market prices and acceptable risk thresholds. We obtain a direct and a dual description of market-consistent prices with acceptable risk. The dual characterisation requires an appropriate extension of the classical fundamental theorem of asset pricing where the role of arbitrage opportunities is played by good deals, i.e., costless investment opportunities with acceptable risk–reward tradeoff. In particular, we highlight the importance of scalable good deals, i.e., investment opportunities that are good deals regardless of their volume.

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Fundamental theorem of asset pricing with acceptable risk in markets with frictions

Arduca

Munari

2023

Finance Stoch

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The countable sup property for lattices of continuous functions

Kandić

Vavpetič

2018

Journal of Mathematical Analysis and Applications

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In this paper we find sufficient and necessary conditions under which vector lattice C(X) and its sublattices C b (X), C 0 (X) and C c (X) have the countable sup property. It turns out that the countable sup property is tightly connected to the countable chain condition of the underlying topological space X. We also consider the countable sup property of C(X × Y ). Even when both C(X) and C(Y ) have the countable sup property it is possible that C(X × Y ) fails to have it. For this construction one needs to assume the continuum hypothesis. In general, we present a positive result in this direction and also address the question when C( λ∈Λ X λ ) has the countable sup property. Our results can be understood as vector lattice theoretical versions of results regarding products of spaces satisfying the countable chain condition. We also present new results for general vector lattices that are of an independent interest.2010 Mathematics Subject Classification. 46B42, 06E10, 46A40, 46E25.

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Smallest order closed sublattices and option spanning

Gao

Leung

2017

Proc. Amer. Math. Soc.

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Let Y be a sublattice of a vector lattice X. We consider the problem of identifying the smallest order closed sublattice of X containing Y . It is known that the analogy with topological closure fails. Let Y o be the order closure of Y consisting of all order limits of nets of elements from Y . Then Y o need not be order closed. We show that in many cases the smallest order closed sublattice containing Y is in fact the second order closure Y o o. Moreover, if X is a σorder complete Banach lattice, then the condition that Y o is order closed for every sublattice Y characterizes order continuity of the norm of X. The present paper provides a general approach to a fundamental result in financial economics concerning the spanning power of options written on a financial asset.This notion that options complete markets, pioneered by Ross, is at the core of modern financial economics ([4]), and has been under extensive exploration.

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Option spanning beyond $$L_p$$ L p -models

Cited by 5 publications

References 36 publications

Fundamental theorem of asset pricing with acceptable risk in markets with frictions

Fundamental theorem of asset pricing with acceptable risk in markets with frictions

The countable sup property for lattices of continuous functions

Smallest order closed sublattices and option spanning

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