A general theory of option pricing: Explicit formulas

Change of Numeraire

Arbitrage Theory in Continuous Time ◽

10.1093/oso/9780198851615.003.0015 ◽

2019 ◽

pp. 202-218

Author(s):

Tomas Björk

Keyword(s):

General Theory ◽

Option Pricing ◽

General Formula ◽

Financial Derivatives ◽

Martingale Measure ◽

Girsanov Transformation ◽

Suitable Change ◽

Pricing Formula ◽

Exchange Option ◽

Numeraire Portfolio

In this chapter we discuss how a suitable change of numeraire and the corresponding change of martingale measure, can simplify the computation of pricing formula for financial derivatives. We derive a general formula for the likelihood process related to an arbitrary numeraire, and we identify the corresponding Girsanov transformation. As an example, we compute the price of an exchange option. In particular we study the class of forward measures related to zero coupon bonds and we derive a general option pricing formula. As an application of the general theory we also study the so-called numeraire portfolio.

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A General Theory of Option Pricing

SSRN Electronic Journal ◽

10.2139/ssrn.3291664 ◽

2018 ◽

Author(s):

David Gershon

Keyword(s):

General Theory ◽

Option Pricing

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Transformations of second order ordinary and partial difierential operators

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500019910 ◽

1982 ◽

Vol 92 (1-2) ◽

pp. 31-49

Author(s):

Calvin D. Ahlbrandt ◽

Don B. Hinton ◽

Roger T. Lewis

Keyword(s):

General Theory ◽

Differential Operators ◽

Second Order ◽

Liouville Type ◽

Explicit Formulas ◽

Partial Differential ◽

First Order ◽

Partial Differential Operators ◽

Unitary Transformations

SynopsisLiouville type transformations are given for symmetric linear ordinary and partial differential operators of second order. Explicit formulas are given for the coefficients of the transformed operators. As a corollary to the general theory we obtain an “Atkinson form” for certain first order vector partial differential operators. This leads to a generalization of the concept of “g-unitary” transformations. Applications to oscillation and spectral theories are included.

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Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

Behavioral and Brain Sciences ◽

10.1017/s0140525x18001620 ◽

2018 ◽

Vol 41 ◽

Cited By ~ 2

Author(s):

Daniel Crimston ◽

Matthew J. Hornsey

Keyword(s):

General Theory ◽

Biological Markers ◽

Natural Environment ◽

Relevant Dimension ◽

Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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