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THE DERIVATIVE
Derivative of usual functions . Graphically the derivative of a function corresponds to the slope of its tangent line at one specific point.
Derivatives markets products and participants: an overview
and quality to enhance the understanding of derivatives markets. This chapter provides an overview of http://www.berkshirehathaway.com/2002ar/2002ar.pdf.
Page 1 of 23 Understanding Financial Derivatives Professor
What is a Financial Derivative? It is a financial instrument. Which derives its value from the underlying asset. e.g. a forward contract on gold
FR01/2015 Risk Mitigation Standards for Non-centrally Cleared OTC
Jan 28 2558 BE the-counter (OTC) derivatives from the International Organization of Securities ... http://www.iosco.org/library/pubdocs/pdf/IOSCOPD423.pdf.
(Translation) - DERIVATIVES ACT BE 2546 (2003)
Any derivatives contract entered into with or through a derivatives business operator a derivatives exchange or a derivatives clearing house shall constitute a
THE PAYMENT SYSTEM - PAYMENTS SECURITIES AND
Sep 30 2553 BE 3 Securities and derivatives trading in the euro area ... Table 20 Share of EU counterparties in the global OTC derivatives market 217.
Framework for supervisory information about derivatives and trading
supervision of the trading and derivatives activities of banks and securities firms and in adequate public disclosure of these activities.
Financial Derivatives
The value of a financial derivative derives from the price of an underlying item such as an asset or index. Unlike debt instruments
Board Oversight of Derivatives (pdf) July 2008
Independent Directors Council. Task Force Report. July 2008. Board Oversight of Derivatives. The voice of fund directors at the Investment Company Institute
Margin requirements for non-centrally cleared derivatives
Non-centrally cleared derivatives contracts should be subject to higher capital www.g20civil.com/documents/Cannes_Declaration_4_November_2011.pdf.
831_2The_derivative.pdf Page1sur13
THEDERIVATIVE
Summary
1.Derivativeofusualfunctions...................................................................................................3
1.1.Constantfunction............................................................................................................3
1.2.Identityfunctionࢌሺ࢞ሻൌ ࢞............................................................................................3
1.3.Afunctionattheform࢞
................................................................................................31.4.Exponentialfunction(oftheformࢇ࢞withࢇ Ͳ):......................................................5
1.5.Functionࢋ࢞
......................................................................................................................5
1.6.Logarithmicfunction࢞...............................................................................................5
2.Basicderivationrules..............................................................................................................6
2.1.Multipleconstant............................................................................................................6
2.2.Additionandsubtractionoffunctions............................................................................6
2.3.Product
offunctionsrule.................................................................................................7
2.4.Quotientoffunctionsrule...............................................................................................8
3.Derivativeofcompositefunctions..........................................................................................9
Howdowerecognizeacompositefunction?.............................................................................9
3.1.Thechainrule..................................................................................................................9
3.2.Chainderivativesofusualfunctions..............................................................................10
4.Evaluationoftheslopeofthetangentatonepoint.............................................................12
5.Increasinganddecreasingfunctions.....................................................................................12
Theslopeconceptusuallypertainstostraightlines.Thedefinitionofastraightlineisa functionforwhichtheslopeisconstant.Inotherwords,nomatterwhichpointweare lookingat,theinclinationofalineremainsthesame.WhenafunctionisnonͲlinear,its slopemayvaryfromonepointtothenext.Wemustthereforeintroducethenotionof derivatewhichallowsustoobtaintheslopeatallpointsofthesenonͲlinearfunctions.Page2of13
Definition
Thederivativeofafunctionfatapointݔ,written݂ඁሺݔሻ,isgivenby: ݂ ඁ ሺݔሻൌο௫՜
݂ሺݔοݔሻെ ݂ሺݔሻοݔ
ifthislimitexists. Graphically,thederivativeofafunctioncorrespondstotheslopeofitstangentlineat onespecificpoint.Thefollowingillustrationallowsustovisualisethetangentline(in blue)ofagivenfunctionattwodistinctpoints.Notethattheslopeofthetangentline variesfromonepointtothenext.Thevalueofthederivativeofafunctiontherefore dependsonthepointinwhichwedecidetoevaluateit.Byabuseoflanguage,weoften speakoftheslopeofthefunctioninsteadoftheslopeofitstangentline.Notation
Here, werepresentthederivativeofafunctionbyaprimesymbol.Forexample,writing݂ඁሺݔሻrepresentsthederivativeofthefunction݂evaluatedatpointݔ.Similarly,writing
ሺ͵ݔ ʹሻඁindicateswearecarryingoutthederivativeofthefunction͵ݔ ʹ.Theprime
symboldisappearsassoonasthe derivativehasbeencalculated.