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Liquidity risk and no arbitrage
Thesis (MSc)--Stellenbosch University, 2013.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2013
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| _version_ | 1867613766978371584 |
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| access_status_str | Open Access |
| author | El Ghandour, Laila |
| author2 | Ouwehand, Peter |
| author_browse | El Ghandour, Laila Ouwehand, Peter |
| author_facet | Ouwehand, Peter El Ghandour, Laila |
| author_sort | El Ghandour, Laila |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2013. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/79975 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:41:21.859Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/79975 Liquidity risk and no arbitrage El Ghandour, Laila Ouwehand, Peter Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Arbitrage pricing theory Fundamental theorems of asset pricing Black-Scholes model Liquidity risk Dissertations -- Mathematics Theses -- Mathematics Capital assets pricing model Arbitrage Pricing Liquidity (Economics) Thesis (MSc)--Stellenbosch University, 2013. ENGLISH ABSTRACT: In modern theory of finance, the so-called First and Second Fundamental Theorems of Asset Pricing play an important role in pricing options with no-arbitrage. These theorems gives a necessary and sufficient conditions for a market to have no-arbitrage and for a market to be complete. An early version of the First Fundamental Theorem of Asset Pricing was proven by Harrison and Kreps [30] in the case of a finite probability space. A more general version was proven by Harrison and Pliska [31] in the case of a finite probability space and discrete time. In the case of continuous time, Delbaen and Schachermayer [19] introduced a more general concept of no-arbitrage called "No-Free Lunch With Vanishing Risk" (NFLVR), and showed that for a locally-bounded semimartingale price process NFLVR is essentially equivalent to the existence of an equivalent local martingale measure. The goal of this thesis is to review the theory of arbitrage pricing and the extension of this theory to include liquidity risk. At the current time, liquidity risk is a key challenge faced by investors. Consequently there is a need to develop more realistic pricing models that include liquidity risk. We present an approach to liquidity risk by Çetin, Jarrow and Protter [10]. In to this approach the liquidity risk is embedded into the classical theory of arbitrage pricing by having investors act as price takers, and assuming the existence of a supply curve where prices depend on trade size. This framework assumes that the quantity impact on the price transacted is momentary. Using trading strategies that are both continuous and of finite variation allows one to avoid liquidity costs. Therefore, the First and Second Fundamental Theorems of Asset Pricing and the Black-Scholes model can be extended. AFRIKAANSE OPSOMMING: In moderne finansiële teorie speel die sogenaamde Eerste en Tweede Fundamentele Stellings van Bateprysbepaling ’n belangrike rol in die prysbepaling van opsies in arbitrage-vrye markte. Hierdie stellings gee nodig en voldoende voorwaardes vir ’n mark om vry van arbitrage te wees, en om volledig te wees. ’n Vroeë weergawe van die Eerste Fundamentele Stelling was deur Harrison en Kreps [30] bewys in die geval van ’n eindige waarskynlikheidsruimte. ’n Meer algemene weergawe was daarna gepubliseer deur Harrison en Pliska [31] in die geval van ’n eindige waarskynlikheidsruimte en diskrete tyd. In die geval van kontinue tyd het Delbaen en Schachermayer [19] ’n meer algemene konsep van arbitragevryheid ingelei, naamlik “No–Free–Lunch–With–Vanishing–Risk" (NFLVR), en aangetoon dat vir lokaalbegrensde semimartingaalprysprosesse NFLVR min of meer ekwivalent is aan die bestaan van ’n lokaal martingaalmaat. Die doel van hierdie tesis is om ’n oorsig te gee van beide klassieke arbitrageprysteorie, en ’n uitbreiding daarvan wat likideit in ag neem. Hedendaags is likiditeitsrisiko ’n vooraanstaande uitdaging wat beleggers die hoof moet bied. Gevolglik is dit noodsaaklik om meer realistiese modelle van prysbepaling wat ook likiditeitsrisiko insluit te ontwikkel. Ons bespreek die benadering van Çetin, Jarrow en Protter [10], waar likiditeitsrisiko in die klassieke arbitrageprysteorie ingesluit word deur die bestaan van ’n aanbodkromme aan te neem, waar pryse afhanklik is van handelsgrootte. In hierdie raamwerk word aangeneem dat die impak op die transaksieprys slegs tydelik is. Deur gebruik te maak van handelingsstrategië wat beide kontinu en van eindige variasie is, is dit dan moontlik om likiditeitskoste te vermy. Die Eerste en Tweede Fundamentele Stellings van Bateprysbepaling en die Black–Scholes model kan dus uitgebrei word om likiditeitsrisiko in te sluit. 2013-02-14T08:44:46Z 2013-03-15T07:29:12Z 2013-02-14T08:44:46Z 2013-03-15T07:29:12Z 2013-03 Thesis http://hdl.handle.net/10019.1/79975 en_ZA Stellenbosch University 107 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Arbitrage pricing theory Fundamental theorems of asset pricing Black-Scholes model Liquidity risk Dissertations -- Mathematics Theses -- Mathematics Capital assets pricing model Arbitrage Pricing Liquidity (Economics) El Ghandour, Laila Liquidity risk and no arbitrage |
| title | Liquidity risk and no arbitrage |
| title_full | Liquidity risk and no arbitrage |
| title_fullStr | Liquidity risk and no arbitrage |
| title_full_unstemmed | Liquidity risk and no arbitrage |
| title_short | Liquidity risk and no arbitrage |
| title_sort | liquidity risk and no arbitrage |
| topic | Arbitrage pricing theory Fundamental theorems of asset pricing Black-Scholes model Liquidity risk Dissertations -- Mathematics Theses -- Mathematics Capital assets pricing model Arbitrage Pricing Liquidity (Economics) |
| url | http://hdl.handle.net/10019.1/79975 |
| work_keys_str_mv | AT elghandourlaila liquidityriskandnoarbitrage |