A Nonstandard Approach to Option Pricing
Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial ec...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cutland, Nigel [verfasserIn] Kopp, Ekkehard [verfasserIn] Willinger, Walter [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Erschienen: |
Oxford, UK: Blackwell Publishing Ltd ; 1991 |
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Online-Ressource |
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| Reproduktion: |
2006 ; Blackwell Publishing Journal Backfiles 1879-2005 |
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In: Mathematical finance - Oxford [u.a.] : Wiley-Blackwell, 1991, 1(1991), 4, Seite 0 |
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volume:1 ; year:1991 ; number:4 ; pages:0 |
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| DOI / URN: |
10.1111/j.1467-9965.1991.tb00017.x |
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| 520 | |a Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. | ||
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10.1111/j.1467-9965.1991.tb00017.x doi (DE-627)NLEJ241820928 DE-627 ger DE-627 rakwb Cutland, Nigel verfasserin aut A Nonstandard Approach to Option Pricing Oxford, UK Blackwell Publishing Ltd 1991 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. 2006 Blackwell Publishing Journal Backfiles 1879-2005 |2006|||||||||| option pricing Kopp, Ekkehard verfasserin aut Willinger, Walter verfasserin aut In Mathematical finance Oxford [u.a.] : Wiley-Blackwell, 1991 1(1991), 4, Seite 0 Online-Ressource (DE-627)NLEJ243926227 (DE-600)1481288-5 1467-9965 nnns volume:1 year:1991 number:4 pages:0 http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 1 1991 4 0 |
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10.1111/j.1467-9965.1991.tb00017.x doi (DE-627)NLEJ241820928 DE-627 ger DE-627 rakwb Cutland, Nigel verfasserin aut A Nonstandard Approach to Option Pricing Oxford, UK Blackwell Publishing Ltd 1991 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. 2006 Blackwell Publishing Journal Backfiles 1879-2005 |2006|||||||||| option pricing Kopp, Ekkehard verfasserin aut Willinger, Walter verfasserin aut In Mathematical finance Oxford [u.a.] : Wiley-Blackwell, 1991 1(1991), 4, Seite 0 Online-Ressource (DE-627)NLEJ243926227 (DE-600)1481288-5 1467-9965 nnns volume:1 year:1991 number:4 pages:0 http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 1 1991 4 0 |
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10.1111/j.1467-9965.1991.tb00017.x doi (DE-627)NLEJ241820928 DE-627 ger DE-627 rakwb Cutland, Nigel verfasserin aut A Nonstandard Approach to Option Pricing Oxford, UK Blackwell Publishing Ltd 1991 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. 2006 Blackwell Publishing Journal Backfiles 1879-2005 |2006|||||||||| option pricing Kopp, Ekkehard verfasserin aut Willinger, Walter verfasserin aut In Mathematical finance Oxford [u.a.] : Wiley-Blackwell, 1991 1(1991), 4, Seite 0 Online-Ressource (DE-627)NLEJ243926227 (DE-600)1481288-5 1467-9965 nnns volume:1 year:1991 number:4 pages:0 http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 1 1991 4 0 |
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10.1111/j.1467-9965.1991.tb00017.x doi (DE-627)NLEJ241820928 DE-627 ger DE-627 rakwb Cutland, Nigel verfasserin aut A Nonstandard Approach to Option Pricing Oxford, UK Blackwell Publishing Ltd 1991 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. 2006 Blackwell Publishing Journal Backfiles 1879-2005 |2006|||||||||| option pricing Kopp, Ekkehard verfasserin aut Willinger, Walter verfasserin aut In Mathematical finance Oxford [u.a.] : Wiley-Blackwell, 1991 1(1991), 4, Seite 0 Online-Ressource (DE-627)NLEJ243926227 (DE-600)1481288-5 1467-9965 nnns volume:1 year:1991 number:4 pages:0 http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 1 1991 4 0 |
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10.1111/j.1467-9965.1991.tb00017.x doi (DE-627)NLEJ241820928 DE-627 ger DE-627 rakwb Cutland, Nigel verfasserin aut A Nonstandard Approach to Option Pricing Oxford, UK Blackwell Publishing Ltd 1991 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. 2006 Blackwell Publishing Journal Backfiles 1879-2005 |2006|||||||||| option pricing Kopp, Ekkehard verfasserin aut Willinger, Walter verfasserin aut In Mathematical finance Oxford [u.a.] : Wiley-Blackwell, 1991 1(1991), 4, Seite 0 Online-Ressource (DE-627)NLEJ243926227 (DE-600)1481288-5 1467-9965 nnns volume:1 year:1991 number:4 pages:0 http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 1 1991 4 0 |
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Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. |
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Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. |
| abstract_unstemmed |
Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ241820928</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210707142427.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">120427s1991 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1111/j.1467-9965.1991.tb00017.x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ241820928</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cutland, Nigel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A Nonstandard Approach to Option Pricing</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford, UK</subfield><subfield code="b">Blackwell Publishing Ltd</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="d">2006</subfield><subfield code="f">Blackwell Publishing Journal Backfiles 1879-2005</subfield><subfield code="7">|2006||||||||||</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">option pricing</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kopp, Ekkehard</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Willinger, Walter</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Mathematical finance</subfield><subfield code="d">Oxford [u.a.] : Wiley-Blackwell, 1991</subfield><subfield code="g">1(1991), 4, Seite 0</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ243926227</subfield><subfield code="w">(DE-600)1481288-5</subfield><subfield code="x">1467-9965</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:1</subfield><subfield code="g">year:1991</subfield><subfield code="g">number:4</subfield><subfield code="g">pages:0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://dx.doi.org/10.1111/j.1467-9965.1991.tb00017.x</subfield><subfield code="q">text/html</subfield><subfield code="x">Verlag</subfield><subfield code="z">Deutschlandweit zugänglich</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DJB</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">1</subfield><subfield code="j">1991</subfield><subfield code="e">4</subfield><subfield code="h">0</subfield></datafield></record></collection>
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