INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS


 Milo Burke
 2 years ago
 Views:
Transcription
1 INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in the cleaing pocess opeated by LCH.Cleanet. It is a commecial pesentation of one of the sevice to be povided by and not a binding commecial offe. Although all easonable cae has been taken in the pepaation of this document LCH.Cleanet disclaims liability of the infomation and fo the uses to which it is put. The document might be upgaded along the poject implementation peiod. Copyight All the intellectual popety ights of the technical pesentation and the diagams included in this document ae vested in. This wok is issued in confidence fo the pupose fo which it is supplied. It must not be epoduced in whole o in pat o used fo othe puposes except with the consent in witing of and then only on the condition that this notice is included in any such epoduction. The infomation that is pat of the document is solely fo infomation pupose and is not to be constued as technical specification.
2 CONTENTS CONTENTS INTRODUCTION... 3 SUMMARY OF CHANGES... 4 CHAPTER I CALCULATION OF RISK ARRAY VALUES... 5 PRINCIPLE USED: MARKET PREMIUM AND THEORETICAL PREMIUM VALUATION... 6 ) Option value:... 6 ) Risk aay theoetical option value ) Risk aay value... 6 CHAPTER II VALUATION FORMULA FOR OPTIONS ON FUTURES AND INDICES... 7 ALGORITHM USED: THEORETICAL PREMIUM AND DELTA Notation Theoetical pemium Delta... 9 CHAPTER III VALUATION FORMULA FOR EQUITY OPTIONS... 0 ALGORITHM USED: THEORETICAL PREMIUM AND DELTA.... Notation... Theoetical pemium Delta... 3 CHAPTER IV VALUATION FORMULA FOR CURRENCY OPTIONS... 4 ALGORITHM USED: THEORETICAL PREMIUM AND DELTA Notation Theoetical pemium Delta... 6
3 INTRODUCTION INTRODUCTION The pupose of the SPAN appendix is to povide infomation about how to pocess isk aay calculation fo end of day and intaday calculation. In addition, this document descibes the diffeences between the new elease (fom the 30 th mach 0) coesponding to UCS V9 & SPAN RMC and the pevious one (befoe the 30 th Mach 0) coesponding to UCSV5 & SPAN. Fistly, you will find a summay of the changes, then, in the fomulas, the detailed of the changes highlighted in yellow. Please note that the main pinciples of the picing models emain unchanged and that the diffeences ae elying on how inputs data ae used within these fomulas.
4 SUMMARY OF CHANGES SUMMARY OF CHANGES Lot size Fo calculation pupose, the lot size used in the calculation was the one of the contact in the pevious elease wheeas in the new elease, it is the lot size of the seies. Inteest ate The inteest ate (including foeign inteest ate when exist) is no longe conveted to natual logaithm (Napieian logaithm) of the calculation fo continuous models as Black 76 model and Gaman Kohlhagen model. Fo discete models such as Cox Ross Rubinstein (Euopean and Ameican style), thee is no impact. Time to matuity Fo each scenaio and to calculate the delta, one day in faction of yea is deducted fom the time to matuity of the option. So, in compaison to the pevious vesion, it is euied to decement life time by (please efe to the fomulas below). Numbe of iteation fo Cox Ross modeling Fo discete models such as Cox Ross Rubinstein (Euopean and Ameican style), thee is a numbe of iteation which is fixed to 30 whateve the model. This is a significant modification compaed to the pevious situation whee accoding to the type of picing model (Ameican: n=7; Euopean: n=30), an aveage was done between n and (n+) iteations. In this new vesion thee is no moe aveage. The 30 iteations have just to be taken into account alone. UCS V9 & SPAN RMC UCSV5 & SPAN  Contact value facto (standing fo lot size) The Contact Value Facto is collected at seies level a. Thee is no Contact Value Facto at contact level in SPAN RMC. One contact value facto is selected fom SPAN file ecod 83 and set as seies contact value facto. b. So fo the whole seies, the Contact Value Facto will be uniue. The time to matuity of the option seies is decemented by one calenda day (/365 = ) fo the scenaio picing. So, T = Time to matuity Time to matuity 3  Inteest ate The Contact Value Facto is collected at contact level a. The Contact Value Facto is detemined at contact level even if it exists at seies level. b. Fo calculation pupose, it is the value at contact level which is used. The time to matuity of each option is taken into account fo the scenaio picing. So, T = Time to matuity Fo option on futues contacts, options on index Fo calculation : option on futues contacts, and cuency options: options on index and cuency options: The value is loaded diectly fom UCS (5 fists  Rd : Yealy continuous financing domestic ate digits) an used without any convesion on the time to matuity of the option ( d = Ln(+  Rd : Yealy continuous financing domestic ate Rd) whee Rd is the yealy financing domestic on the time to matuity of the option ate)  Rf : Yealy continuous financing foeign ate on  Rf : Yealy continuous financing foeign ate on the time to matuity of the option the time to matuity of the option ( f = Ln(+ Rf) Fo option on stocks: no gap. whee Rf is the yealy financing foeign ate) Fo option on stocks: no gap. 4  Numbe of iteation The numbe of iteation is a Cox Ross Rubinstein input paamete The numbe of iteation is no longe depending on the contact. A paamete is set as default whateve the contact: Euopean and Ameican type Cox Ross Rubinstein iteation = 30 The numbe of iteation depends on the contact: a. Euopean type Cox Ross Rubinstein iteation = 30 b. Ameican type Cox Ross Rubinstein iteation = 7
5 CALCULATION OF RISK ARRAY VALUES CHAPTER I CALCULATION OF RISK ARRAY VALUES
6 CALCULATION OF RISK ARRAY VALUES A isk aay can be defined as a set of numbes: Fo a paticula contact At a paticula point in time To be magined fo a paticula business function Fo a paticula account. Each isk aay value specifies how a single long o shot position will lose o gain value if the coesponding isk scenaio occus ove the specified lookahead time. The lookahead time is the aveage time pe day. So it eflects the unit of time into the futue fom the cuent time. By convention, losses fo long positions ae expessed as positive numbes, and gains as negative numbes. PRINCIPLE USED: MARKET PREMIUM AND THEORETICAL PREMIUM VALUATION ) Option value:.) Fo endofday: Option is valued using as inputs: a. Maket pice (o pemium) value of the option poduct (conveted to option cuency if needed and scaled to the option size): (Maket pice * option CVF)..) Fo intaday: Theoetical option value is calculated using as inputs: a. Value of the undelying poduct (conveted to option cuency if need be and scaled to the option size): (undelying pice * undelying CVF) * Cuency convesion ate * option scaling facto. (Option scaling facto is eual to option CVF/undelying CVF) b. Option implied volatility c. Option stike value: (stike * option CVF) d. Time to matuity e. Inteest ate f. Dividends ) Risk aay theoetical option value Fo each isk aay point new theoetical value is calculated using as inputs: a. Value of the undelying poduct (conveted to option cuency if need be and scaled appopiately if CVF fo undelying and CVF fo options ae diffeent): (undelying pice * undelying CVF + pice scan ange * faction )* cuency convesion ate * option scaling facto. b. Option implied volatility + volatility scan ange * faction c. Option stike value: (stike * option CVF) d. Time to matuity move ahead time e. Inteest ate f. Dividends 3) Risk aay value 3.) Fo endofday: Fo each isk aay point diffeence between valued maket pice and theoetical option value is taken as isk aay value. 3.) Fo intaday: Fo each isk aay point diffeence between theoetical value calculated fo this point and theoetical option value is taken as isk aay value. Fom this desciption it is clea that: Risk aay values will always come out appopiately scaled (in the option value tems). Pice scan ange as input in this algoithm has to be specified in undelying value tems.
7 VALUATION FORMULA FOR OPTIONS ON FUTURES AND INDICES CHAPTER II VALUATION FORMULA FOR OPTIONS ON FUTURES AND INDICES
8 VALUATION FORMULA FOR OPTIONS ON FUTURES AND INDICES Fo detemining the initial magin euied to cove the positions on options on futues contacts (commodity fo instance) and options on index, uses a theoetical pemium valuation fomula of the type Black 76. ALGORITHM USED: THEORETICAL PREMIUM AND DELTA. Notation The algoithm euies the following data: U E T 0 T R N(x) Ln e : Pice of the undelying futues contact of the option : Stike pice of the option : Time to matuity of the option (in faction of yea (base: 365 d o 366 d)). : A time to matuity minus the lookahead time of the option. The lookahead time is aveage time pe day (base: (/365) d o ). So it eflects the unit of time (in faction of yea) into the futue fom the cuent time ( T T0 moveahead o T ) : Yealy volatility of the undelying (expessed in %). : Yealy continuous financing ate on the life span of the option : Distibution function of the nomal law : Napieian logaithm : exponential function T 0. Theoetical pemium The call pemium and the put pemium on the commodities futues contact and index ae expessed as follows: C e R* T * U * N( d) E * N( d) P e R* T * U * ( N( d) ) E * ( N( d) ) Whee d U * Ln * v T v * T E * d d v * T In ode to simplify the fomula, the nomal law is appoximated with a fifth degee polynomial such as: P( d) * e whee: d * ( bx cx fx 3 gx 4 ix 5 ) x a * d and a = b = c = f = g = i =
9 VALUATION FORMULA FOR OPTIONS ON FUTURES AND INDICES Then: if d > 0 N(d) = P(d) if d 0 N(d) = P(d) Note: Option theoetical pemium Fo intaday calculation, theoetical pemiums ae pefomed befoe isk aay calculation. Theefoe the fomula is the same except that T 0 is used instead of T. Contolling via the intinsic value of the option If the Black 76 fomula gives a theoetical pemium that is infeio to the intinsic value, the pemium selected fo detemining the initial magin shall coespond to: The intinsic value if the execise style of the option is Ameican style The theoetical pemium if the execise style of the option is Euopean style. Rounding off The calculated isk aays values elated to SPAN scenaios ae ounded off to two decimals. 3. Delta The call delta and the put delta fo the long ate and commodities futues contact and index ae expessed as follows: Call * N( d) Put * N( d) e RT e RT Rounding off The calculated delta is ounded off to fou decimals.
10 VALUATION FORMULA FOR EQUITY OPTIONS CHAPTER III VALUATION FORMULA FOR EQUITY OPTIONS
11 VALUATION FORMULA FOR EQUITY OPTIONS As pat of detemining the initial magin euied to cove the positions on euity stock options contacts, uses a theoetical pemium valuation fomula of the type Cox Ross Rubinstein. ALGORITHM USED: THEORETICAL PREMIUM AND DELTA. Notation S : Index o settlement pices of the undelying contact of the option E : Stike pice of the option T 0 : Time to matuity of the option (in faction of yea (base: 365 d o 366 d)). t : Time to matuity of the option minus the lookahead time of the option. The lookahead time is aveage time pe day (base: (/365) d o ). So it eflects the unit of time (in faction of yea) into the futue fom the cuent time ( T T0 moveahead o T ) R t n h s T 0s t s : Yealy volatility of the undelying (expessed in %). : Financing ate coesponding to the life span of the options. : Numbe of iteations used in the model. n =30 iteations. : Amount of the dividend distibuted to the iteation s (the model accepts 8 payments of dividends pe yea) : numbe of days left befoe the payment of the dividend h s. The numbe is expessed in faction of yeas (base: 365 d o 366 d) : numbe of days left afte applying the lookahead time and befoe the payment of the dividend h s. The numbe is expessed in faction of yeas (base: 365 d o 366 d) ( t T moveahead s 0 s o t s T 0s ) Definition of intemediay data R t t n is the continuous inteest ate Definition of the neutal isk pobability If no dividend is paid duing the life span of the option, the neutal isk pobability is: T 0 u d d whee v e t n u, and d u If the occuence s fo the payment of the dividend h s coesponds to the iteation i, the neutal isk pobability becomes: h i i j u * S i, j, i n et j i u d whee i = s h s is the amount of the dividend distibuted at the iteation s. t The iteation s is the intege pat of n* s. t Note: if the iteation i = s, no dividend is paid (h i=s =0). In that case, the neutal isk pobability is eual to.
12 VALUATION FORMULA FOR EQUITY OPTIONS Dividend management fo option valuation: in case thee is not a full distibution of dividends detached ove the complete option lifetime, the last known dividend value eceived fo an option instument will be used and duplicated until the matuity date of the option as often as possible fom the last known detachment date accoding to a cetain feuency type. Thee types of feuency can be applied and ae expessed in numbe of days: yealy (365 days), halfyealy (8 days), uately (9 days).this feuency type is defined at the combined commodity level in the magin paametes and follows the maket ules (e.g. Pais secuities geneally detach a yealy dividend). C i,j (espectively P i,j ) is the pice of the call (esp. put) at the iteation i in the hypothesis j consideing the cost evolution of the undelying instument. Theoetical pemium The theoetical pemium fo each scenaio is pefomed with 30 iteations. As the n+ C n,j pices (espectively P n,j ) at the call month date (esp. put) coesponding to the iteation n and to each hypotheses j consideing the cost evolution of the undelying instument ae known, the theoetical pemium is calculated fom the following ecuence fomula afte n iteations, and diffeentiating the Euopean and the Ameican chaacte of the option.. Euopean options (30 iteations) At expiy, Call At expiy, Put n j Cn, j max 0, u * S fo j=,,n+ E n j Pn, j max 0, E u * S fo j=,,n+ C i, j i, j * C i, j i, j * C i, j P i, j i, j * P i, j i, j * P i, j fo i = n, n,,, 0 et j =,,, i, i+ Theoetical pemium at the valuation moment fo i = n, n,,, 0 et j =,,, i, i+ Theoetical pemium at the valuation moment C 0, 0, * C, 0, * C, P 0, 0, * P, 0, * P, Note: Option theoetical pemium Fo intaday calculation, theoetical pemiums ae pefomed befoe isk aay calculation. Theefoe the fomula is the same except that T 0 is used instead of t. Rounding off The calculated isk aays values elated to SPAN scenaios ae ounded off to two decimals.. Ameican options (30 iteations) At expiy, Call At expiy, Put
13 VALUATION FORMULA FOR EQUITY OPTIONS n j Cn, j max 0, u * S fo j=,,n+ E n j Pn, j max 0, E u * S fo j=,,n+ i, j * Ci, j i, j * Ci, j n j Ci, j max, u * S E fo i = n, n,,, 0 et j =,,, i, i+ Theoetical pemium at the valuation moment i, j * Ci, j i, j * Pi, j n j Pi, j max, E u * S fo i = n, n,,, 0 et j =,,, i, i+ Theoetical pemium at the valuation moment 0, * C, 0, * C, C 0, max, S E 0, * C, 0, * P, P 0, max, E S Note: Option theoetical pemium Fo intaday calculation, theoetical pemiums ae pefomed befoe isk aay calculation. Theefoe the fomula is the same except that T 0 is used instead of t. Rounding off The calculated isk aays values elated to SPAN scenaios ae ounded off to two decimals. 3. Delta The call delta and the put delta ae calculated as follows: Call Put Call C S x C S x P S x P S Put * x * x x Contolling the pice size The following check value is pefomed on the undelying pice in ode to adapt the accuacy of the delta calculation: By default, the value of the paamete x is set to 0. without valuation. To be consistent, this paamete must be valued with the option CVF (as it is done fo pemiums and maket pice). y* S x, then x y * S Else x is kept unchanged. If By default, the value of y is set to 0. without valuation. To be consistent, this paamete must be valued with the option CVF (as it is done fo pemiums and maket pice). Rounding off The calculated delta is ounded off to fou decimals.
14 VALUATION FORMULA FOR CURRENCY OPTIONS CHAPTER IV VALUATION FORMULA FOR CURRENCY OPTIONS
15 VALUATION FORMULA FOR CURRENCY OPTIONS Fo detemining the initial magin euied to cove the positions on options on cuency futues contacts, uses a theoetical pemium valuation fomula of the type Gaman kohlhagen. ALGORITHM USED: THEORETICAL PREMIUM AND DELTA. Notation The algoithm euies the following data: U E T 0 T R d R f N(x) Ln e : Pice of the undelying futues contact of the option : Stike pice of the option : Time to matuity of the option (in faction of yea (base: 365 d o 366 d)). : A time to matuity minus the lookahead time of the option. The lookahead time is aveage time pe day (base: (/365) d o ). So it eflects the unit of time (in faction of yea) into the futue fom the cuent time ( T T0 moveahead o T ) : Yealy volatility of the undelying (expessed in %). : Yealy continuous financing domestic ate on the life span of the option : Yealy continuous financing foeign ate on the life span of the option : Distibution function of the nomal law : Napieian logaithm : exponential function T 0. Theoetical pemium The call pemium and the put pemium on the cuency futues contact ae expessed as follows: C R * T * T f d U * e * N( d) E * e * N( d) R P R * T * T f d U * e * N( d) E * e * N( d) R Whee R R * T d f U * e d * Ln * v * T d d v * T v * T E In ode to simplify the fomula, the nomal law is appoximated with a fifth degee polynomial such as: P( d) * e d * ( bx cx fx 3 gx 4 ix 5 ) whee:
16 VALUATION FORMULA FOR CURRENCY OPTIONS x a * d and a = b = c = f = g = i = Then: if d > 0 N(d) = P(d) if d 0 N(d) = P(d) Note: Option theoetical pemium Fo intaday calculation, theoetical pemiums ae pefomed befoe isk aay calculation. Theefoe the fomula is the same except that T 0 is used instead of T. Rounding off The calculated isk aays values elated to SPAN scenaios ae ounded off to two decimals. 3. Delta The call delta and the put delta fo the cuency futues contact ae expessed as follows: Call e R T * R T * f f N( d ) e N( d ) Put Rounding off The calculated delta is ounded off to fou decimals.
Chapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationYIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1  P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
More informationBasic Financial Mathematics
Financial Engineeing and Computations Basic Financial Mathematics Dai, TianShy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationCONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
More informationGESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS
GESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 20102011 Chapte 1 The Copoation 113. What is the diffeence
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationEquity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers
Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The
More informationDefinitions. Optimization of online direct marketing efforts. Test 1: Two Email campaigns. Raw Results. Xavier Drèze André Bonfrer. Lucid.
Definitions Optimization of online diect maketing effots Xavie Dèze Andé Bonfe Lucid Easily undestood; intelligible. Mentally sound; sane o ational. Tanslucent o tanspaent. Limpid Chaacteized by tanspaent
More informationIgnorance is not bliss when it comes to knowing credit score
NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news
More informationLoyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationDefine What Type of Trader Are you?
Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationFinancial Planning and Riskreturn profiles
Financial Planning and Risketun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 201016 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risketun
More informationFI3300 Corporate Finance
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multipeiod multicf timevalueofmoney poblems: Geneal case Pepetuity
More informationPersonal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit () Total Private Saving Rate (S Private /Y) 12/18/2009
1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.02.04.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationThe Time Value of Money
he ime Value of Money Inteest Rates and Futue Value Inteest ates ae a facto in the valuation of vitually all financial instuments. While all money maket ates () ae quoted on an annual basis (PR nnual Pecentage
More informationSUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014
SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk  Risk to shaeholdes esulting fom the use of debt. Financial Leveage  Incease in the vaiability of shaeholde etuns that
More informationHEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING
U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 22863540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationcover comparison TUH it s my health fund! Your Queensland health fund Effective 2 April 2014
Effective 2 Apil 2014 You Queensland health fund cove compaison TUH it s my health fund! PLEASE CAREFULLY READ AND RETAIN THIS BROCHURE. PLEASE READ IN CONJUNCTION WITH THE Fine Points BROCHURE. waiting
More informationAn application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty
An application of stochastic pogamming in solving capacity allocation and migation planning poblem unde uncetainty YinYann Chen * and HsiaoYao Fan Depatment of Industial Management, National Fomosa Univesity,
More information867 Product Transfer and Resale Report
867 Poduct Tansfe and Resale Repot Functional Goup ID=PT Intoduction: This X12 Tansaction Set contains the fomat and establishes the data contents of the Poduct Tansfe and Resale Repot Tansaction Set (867)
More informationFirstmark Credit Union Commercial Loan Department
Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo MatínezdeAlbéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationTRADING DAYS IN 2010  LONDON DERIVATIVES MARKET INTRODUCTION
EURONEXT DERIVATIVES MARKETS LONDON MARKET TRADING DAYS IN 2010  LONDON DERIVATIVES MARKET INTRODUCTION An oveview of the Tading Days in 2010 was issued unde London Notice No. 3203 on 13 Octobe 2009.
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationSolutions to Problems: Chapter 7
Solution to Poblem: Chapte 7 P71. P72. P73. P74. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationarxiv:1110.2612v1 [qfin.st] 12 Oct 2011
Maket inefficiency identified by both single and multiple cuency tends T.Toká 1, and D. Hováth 1, 1 Sos Reseach a.s., Stojáenská 3, 040 01 Košice, Slovak Republic Abstact axiv:1110.2612v1 [qfin.st] 12
More informationMATHEMATICAL SIMULATION OF MASS SPECTRUM
MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationConcept and Experiences on using a Wikibased System for Softwarerelated Seminar Papers
Concept and Expeiences on using a Wikibased System fo Softwaeelated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wthaachen.de,
More informationAn Epidemic Model of Mobile Phone Virus
An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity
More informationLife Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More informationContingent capital with repeated interconversion between debt and equity
Contingent capital with epeated inteconvesion between debt and equity Zhaojun Yang 1, Zhiming Zhao School of Finance and Statistics, Hunan Univesity, Changsha 410079, China Abstact We develop a new type
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationSaving and Investing for Early Retirement: A Theoretical Analysis
Saving and Investing fo Ealy Retiement: A Theoetical Analysis Emmanuel Fahi MIT Stavos Panageas Whaton Fist Vesion: Mach, 23 This Vesion: Januay, 25 E. Fahi: MIT Depatment of Economics, 5 Memoial Dive,
More informationFixed Income Attribution: Introduction
18th & 19th Febuay 2015, Cental London Fixed Income Attibution: A compehensive undestanding of Fixed Income Attibution and the challenging data issues aound this topic Delegates attending this twoday
More informationExperimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival
Expeimentation unde Uninsuable Idiosyncatic Risk: An Application to Entepeneuial Suvival Jianjun Miao and Neng Wang May 28, 2007 Abstact We popose an analytically tactable continuoustime model of expeimentation
More informationChris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment
Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability
More information30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research
RAIRO Rech. Opé. (vol. 33, n 1, 1999, pp. 2945) A GOOD APPROXIMATION OF THE INVENTORY LEVEL IN A(Q ) PERISHABLE INVENTORY SYSTEM (*) by Huan Neng CHIU ( 1 ) Communicated by Shunji OSAKI Abstact. This
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationOverencryption: Management of Access Control Evolution on Outsourced Data
Oveencyption: Management of Access Contol Evolution on Outsouced Data Sabina De Capitani di Vimecati DTI  Univesità di Milano 26013 Cema  Italy decapita@dti.unimi.it Stefano Paaboschi DIIMM  Univesità
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationHow to create RAID 1 mirroring with a hard disk that already has data or an operating system on it
AnswesThatWok TM How to set up a RAID1 mio with a dive which aleady has Windows installed How to ceate RAID 1 mioing with a had disk that aleady has data o an opeating system on it Date Company PC / Seve
More informationMERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION
MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION Enique Andeu, Kisten Edwads, Aleando Requeo 1,2 Novembe 2010 Abstact In this aticle we pesent a method that
More informationEffect of Contention Window on the Performance of IEEE 802.11 WLANs
Effect of Contention Window on the Pefomance of IEEE 82.11 WLANs Yunli Chen and Dhama P. Agawal Cente fo Distibuted and Mobile Computing, Depatment of ECECS Univesity of Cincinnati, OH 452213 {ychen,
More informationInsurance Pricing under Ambiguity
Insuance Picing unde Ambiguity Alois Pichle a,b, a Univesity of Vienna, Austia. Depatment of Statistics and Opeations Reseach b Actuay. Membe of the Austian Actuaial Association Abstact Stating fom the
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationSymmetric polynomials and partitions Eugene Mukhin
Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation
More informationTHE DISTRIBUTED LOCATION RESOLUTION PROBLEM AND ITS EFFICIENT SOLUTION
IADIS Intenational Confeence Applied Computing 2006 THE DISTRIBUTED LOCATION RESOLUTION PROBLEM AND ITS EFFICIENT SOLUTION Jög Roth Univesity of Hagen 58084 Hagen, Gemany Joeg.Roth@Fenunihagen.de ABSTRACT
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationLiquidity and Insurance for the Unemployed
Liquidity and Insuance fo the Unemployed Robet Shime Univesity of Chicago and NBER shime@uchicago.edu Iván Wening MIT, NBER and UTDT iwening@mit.edu Fist Daft: July 15, 2003 This Vesion: Septembe 22, 2005
More informationTHE CARLO ALBERTO NOTEBOOKS
THE CARLO ALBERTO NOTEBOOKS Meanvaiance inefficiency of CRRA and CARA utility functions fo potfolio selection in defined contibution pension schemes Woking Pape No. 108 Mach 2009 Revised, Septembe 2009)
More informationPromised LeadTime Contracts Under Asymmetric Information
OPERATIONS RESEARCH Vol. 56, No. 4, July August 28, pp. 898 915 issn 3364X eissn 15265463 8 564 898 infoms doi 1.1287/ope.18.514 28 INFORMS Pomised LeadTime Contacts Unde Asymmetic Infomation Holly
More informationTransmittal 198 Date: DECEMBER 9, 2005. SUBJECT: Termination of the Existing EligibilityFile Based Crossover Process at All Medicare Contractors
anual ystem Depatment of ealth & uman evices (D) entes fo edicae & Pub 10020 OneTime Notification edicaid evices () Tansmittal 198 Date: DEEBE 9, 2005 hange equest 4231 UBJET: Temination of the Existing
More informationModeling and Verifying a Price Model for Congestion Control in Computer Networks Using PROMELA/SPIN
Modeling and Veifying a Pice Model fo Congestion Contol in Compute Netwoks Using PROMELA/SPIN Clement Yuen and Wei Tjioe Depatment of Compute Science Univesity of Toonto 1 King s College Road, Toonto,
More informationAn Infrastructure Cost Evaluation of Single and MultiAccess Networks with Heterogeneous Traffic Density
An Infastuctue Cost Evaluation of Single and MultiAccess Netwoks with Heteogeneous Taffic Density Andes Fuuskä and Magnus Almgen Wieless Access Netwoks Eicsson Reseach Kista, Sweden [andes.fuuska, magnus.almgen]@eicsson.com
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationAutomated Hydraulic Drilling Rigs. HHSeries
Automated Hydaulic Dilling Rigs HHSeies The Shape of Things to Come CUSTOMSOLUTIONS HH600 Rig The HH Hydaulic Hoist Seies Eveything about the HH Seies is designed fo speed, safety and efficiency. You can
More informationCloud Service Reliability: Modeling and Analysis
Cloud Sevice eliability: Modeling and Analysis YuanShun Dai * a c, Bo Yang b, Jack Dongaa a, Gewei Zhang c a Innovative Computing Laboatoy, Depatment of Electical Engineeing & Compute Science, Univesity
More informationTransmittal 47 Date: FEBRUARY 24, 2006
anual ystem Pub 10003 edicae National oveage Deteminations Depatment of Health & Human evices (DHH) ente fo edicae & edicaid evices () Tansmittal 47 Date: EBUAY 24, 2006 hange equest 4257 UBJET: hanges
More informationInstructions to help you complete your enrollment form for HPHC's Medicare Supplemental Plan
Instuctions to help you complete you enollment fom fo HPHC's Medicae Supplemental Plan Thank you fo applying fo membeship to HPHC s Medicae Supplement plan. Pio to submitting you enollment fom fo pocessing,
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationTracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors
Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg
More informationAgenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar
Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The ISLM Model fo an Open Economy Macoeconomic Policy in an Open Economy
More informationHigh Availability Replication Strategy for Deduplication Storage System
Zhengda Zhou, Jingli Zhou College of Compute Science and Technology, Huazhong Univesity of Science and Technology, *, zhouzd@smail.hust.edu.cn jlzhou@mail.hust.edu.cn Abstact As the amount of digital data
More informationCRRC1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer
CRRC Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 21 22 Leaig
More informationFaithful Comptroller s Handbook
Faithful Comptolle s Handbook Faithful Comptolle s Handbook Selection of Faithful Comptolle The Laws govening the Fouth Degee povide that the faithful comptolle be elected, along with the othe offices
More informationTheory and practise of the gindex
Theoy and pactise of the gindex by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,
More information