Valuation and Parities for Exchange Options

Kardaras, Constantinos

doi:10.1137/120884973

Cited by 6 publications

(9 citation statements)

References 34 publications

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“…By reducing things to earlier work of Yan (), they present versions of the first and second FTAP, and they also introduce and study so‐called martingale valuation operators. The corresponding valuation results, for a fixed such operator, are similar to those of Kardaras ().…”

Section: Introductionsupporting

confidence: 71%

“…The earlier paper Carr et al. () has

N = 2

and studies some of the effects that appear in valuation when one of the assets hits 0, with results that look similar to the ones in Kardaras (). The notion of valuation in Carr et al.…”

Section: Examples and Related Workmentioning

confidence: 59%

“…More recently, a number of papers have also examined a similar symmetric setting as our paper. Kardaras () studies valuation and parities for exchange options in a general model with finitely many assets

S^{i} \geq 0

in an economy with a possibly stochastic lifetime ζ. The main assumptions are that

S^{i} = 0

[[ζ, \infty [[

and that there is a nonnegative local martingale deflator Z , i.e., Z and each

Z S^{i}

is a local

double-struckP

‐martingale (and

Z_{0} = 1

).…”

Section: Examples and Related Workmentioning

confidence: 99%

“…The main assumptions are that

S^{i} = 0

[[ζ, \infty [[

and that there is a nonnegative local martingale deflator Z , i.e., Z and each

Z S^{i}

is a local

double-struckP

‐martingale (and

Z_{0} = 1

). By definition, a time‐ T payoff

H_{T}

is then valued at time 0 by

E_{double-struckP} false[Z_{T} H_{T} I_{false{T < ζ false}} false]

, and the focus of Kardaras () is on deriving expressions for this value, when

H_{T} = {(S_{T}^{j} - S_{T}^{i})}^{+}

is an exchange option, in terms of expectations under measures

Q^{i}

and

Q^{j}

under which

S^{i}

respectively

S^{j}

have (almost) a local martingale property. There is no deeper economic justification for the above choice of valuation (nor for the choice of Z , if there are several), and there is no discussion of valuations at later times

t > 0

.…”

Section: Examples and Related Workmentioning

confidence: 99%

“…Here we just mention two recent papers fairly closely related to our work. Kardaras () studies valuation and parities for exchange options in a general model with finitely many assets having nonnegative prices. He fixes a local martingale deflator, defines prices with respect to this, and shows how different terms in the resulting valuation formulas can be given a financial interpretation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Semi‐efficient valuations and put‐call parity

Herdegen

Schweizer

2017

Mathematical Finance

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We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy-and-hold strategies (called static efficiency). A valuation process for a payoff is then called semi-efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk-neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put-call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put-call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory. K E Y W O R D Sabsence of arbitrage, completeness, consistent valuation, efficiency, incomplete markets, maximal strategies, NFLVR, NUPBR, option valuation, put-call parity, risk-neutral valuation, semi-efficient markets, viability Mathematical Finance. 2018;28:1061-1106.wileyonlinelibrary.com/journal/mafi

show abstract

Section: Introductionsupporting

confidence: 71%

“…The earlier paper Carr et al. () has

N = 2

and studies some of the effects that appear in valuation when one of the assets hits 0, with results that look similar to the ones in Kardaras (). The notion of valuation in Carr et al.…”

Section: Examples and Related Workmentioning

confidence: 59%