OpenGamma Documentation Bond Pricing


 Ruby Parrish
 1 years ago
 Views:
Transcription
1 OpenGaa Docuentation Bond Pricing Marc Henrard OpenGaa Docuentation n. 5 Version May 2013
2 Abstract The details of the ipleentation of pricing for fixed coupon bonds and floating rate note are provided. The different day count and yield conventions used by sovereign bonds are described.
3 Contents 1 Introduction 1 2 Notation Fixed coupon bond Floating rate note Conventions Day count: ACT/ACT ICMA Day count: ACT/365 Fixed Sovereign bonds conventions Settleent lag Repurchase agreeent 3 5 Discounting Fixed coupon bond Floating rate note FRN) Clean and dirty price Dirty price of a bond security fro curves Fixed coupon bond present value fro clean price Yield Siple interest in last period Copound interest in last period US Street convention UK: DMO ethod US Treasury Convention FRANCE:COMPND METH GERMAN BONDS Sovereign bonds conventions Duration and convexity Modified duration Macaulay duration Convexity Other easures Zspread Zspread sensitivity Ipleentation 9
4
5 1 Introduction The coputation of the present value of fixed coupon bonds and floating rate notes is not very coplex atheatically. Nevertheless, it requires a lot of details and there are any subtleties. This note provides the details of the ipleentation in the OpenGaa analytical library. When speaking about bonds, one can ake the distinction between a bond security or issue) and a bond transaction. Here, the bond security represents the official description of the bond, with details about the coupons, noinal payents and conventions. A bond transaction is the purchase or sale) of a certain quantity of the bond issue on a given date for a given price. The bond figures described here involves both of those concepts. Fixed coupon bonds are usually quoted as clean prices. The clean price is the relative price to be paid at the standard settleent date in exchange for the bond. Soe bonds trade excoupons before the coupon payent. The coupon is paid not to the owner of the bond on the payent date but to the owner of the bond on the detachent date. The difference between the two is the excoupon period easured in days). The issues related to those detachents are also described. When a bond has been purchased but has not settled yet, the proceeds of the payent are still pending. The payent of those proceeds need to be taken into account in the present value calculation of the bond purchase. The aount representing the proceed will have the opposite sign to the quantity of bond purchased. The total present value of a bond which has not settled will generally be very sall with respect to the notional. 2 Notation The pricing described here will be relative to a reference date denoted t r ; the will be, depending of the circustances described below, the settleent date of a particular transaction, the standard spot date of the bond or today. Only the cash flows after that date subject to excoupon adjustents) will be taken into account. The definition of after will also depend of the circustances: for settle;net date it eans t > t r but for today, it eans t 0 = t r. 2.1 Fixed coupon bond The coupon aounts are denoted c i ),...,n c and paid on ties t c i ); the nuber of coupon periods in a year is denoted. Only the coupons to be received are taken into account. When the excoupon period is 0, the coupons taken into account are the coupons after the reference date. When the excoupon period is nonzero we need an extra date which is t x, the reference date plus the excoupon period. The coupons taken into account are the coupons such that t c i > t x. The notional capital) payents are denoted N i ),...,n N and are paid on t N i ). Usually, there is a unique payent of the full notional at the final coupon date t c nc. But in case of aortising bonds, the notional can be paid in several instalents, The bond settleent purchase) is done through the payent of an aount S on t S. The sign of S is the opposite of the sign of N i. If the settleent has already occurred, the aount used is S = 0 and the tie is t S = 0. 0 First version: 8 April 2011; this version: May
6 2.2 Floating rate note The coupon aounts are denoted Ni c),...,n c; the spreads are sc i, the accrual fraction are δc i and the coupons are paid on t c i ). The coupon payoff is the Ibor rate plus the argin ultiplied by the coupon accrual and notional, i.e. L I i + sc i )δc i N i c. The Ibor fixing accrual fraction is δi i. As for fixed coupon bonds, only the coupons to be received are taken into account. It eans that if the excoupon period is 0, the coupons taken into account are the coupons such that t c i > t r. If the excoupon period is nonzero, let t x be the reference date plus the excoupon period. The coupons taken into account are the coupons such that t c i > t x. The notional capital) payents are denoted N i ),...,n N and are paid in t N i ). Usually there is a unique payent of the full notional at the final coupon date t c n c. The bond settleent purchase) is done through the payent of an aount S in t S. If the settleent already occurred, the aount used is S = 0 and the tie is t S = 0. 3 Conventions The ost used day count conventions for bonds are 3.1 Day count: ACT/ACT ICMA The rule is described in ICMA. The accrual factor is 1 Freq Adjustent where Freq is the nuber of coupon per year and Adjustent depends of the type of stub period. None The Adjustent is 1. The second expression reduces to 1 and the coupon is 1/Freq. Short at start The Adjustent is coputed as a ratio. The nuerator is the nuber of days in the period. The denoinator is the nuber of days between the standardised start date, coputed as the coupon end date inus the nuber of onth corresponding to the frequency i.e. 12/Freq), and the end date. Long at start Two standardised start dates are coputed as the coupon end date inus one tie and two ties the nuber of onth corresponding to the frequency. The nuerator is the nuber of days between the start date and the first standardised start date and the nuerator is the nuber of days between the first and second standardised start date. The Adjustent is the ratio of the nuerator by the denoinator plus 1. Short at end The Adjustent is coputed as a ratio. The nuerator is the nuber of days in the period. The denoinator is the nuber of days between the start date and the standardised end date, coputed as the coupon start date plus the nuber of onth corresponding to the frequency i.e. 12/Freq). Long at end Two standardised end dates are coputed as the coupon start date plus one tie and two ties the nuber of onth corresponding to the frequency. The nuerator is the nuber of days between the end date and the first standardised end date and the nuerator is the nuber of days between the second and first standardised end date. The Adjustent is the ratio of the nuerator by the denoinator plus 1. 2
7 3.2 Day count: ACT/365 Fixed Also called English Money Market basis. The accrual factor is d 2 d where d 2 d 1 is the nuber of days between the two dates. The nuber 365 is used even in a leap year. 3.3 Sovereign bonds conventions The following countries use the ACT/ACT ICMA: France Gerany Italy Spain United Kingdo since Noveber 1, 1998) United States The following countries use the Day count: ACT/365: United Kingdo before Noveber 1, 1998) 3.4 Settleent lag A conventional settleent lag is associated to each bond. The lag is the delay between trade date and settleent date. It is usually one business day for US treasuries and UK Gilts and three days for Euroland governent bonds. transactions can be entered into at any settleent date agreed by the parties. Nevertheless the quoted price fro data providers are prices for standard settleent date. It is iportant to know the correct convention to use the quoted price inforation correctly even if one does not use those conventions for actual transactions. 4 Repurchase agreeent A repurchase agreeent repo) is a collateralised deposit which is financially equivalent to selling and buying back the sae bond at an agreed price at a later date even if there are legal differences between the two). If we take a repo with settleent date today and aturity at a date t r in the future, the flows are given in Table 1. On the other side it is possible to sell the bond today with value date today and at the sae tie buy today with settleent t r. The flows are also given in Table 1. The two being equal, the dirty price with forward settleent is Dirtyt r ) = Dirty0)1 + δr), i.e. the forward price should be discounted at the repo) risk free rate to obtain today s value. We will use this discounting fro settleent approach for the bond when we discuss present value coputation fro quoted price. 3
8 Repo Bond today and forward Tie Cash flow Bond Tie Cash flow Bond 0 +P P 0 1 t r P δr) +1 t r P tr +1 5 Discounting Table 1: Flow for repo and forward settleent bond transaction. The discounting price is the price obtained by discounting each cash flow. Not all cash flows are discounted using the sae curve. The following sections describes the details for coupon bonds and floating rate notes. 5.1 Fixed coupon bond For a coupon bond, all the cash flows are known and directly discounted. The coupons and notional are discounted with the curve including credit risk relevant for the issuer. The settleent aount when the bond has not settled yet) is discounted with the riskfree curve, as the aount to be paid for settleent is collateralised by the bond delivery versus payent DVP)). The two curves used are 1. Discounting risk free) : P D t). 2. Credit issuer): P C t). The present value of the security without settleent payent is, for t c i 0, c n PV Security Discounting = c i P C t c i) + n N N i P C t N i ). 1) If the settleent date t s is after today t s 0) and the settleent aount is S, the present value of a transaction is given by, for t c i > t s, PV Transaction Discounting = c i P C t c i) + n c n N 5.2 Floating rate note FRN) N i P C t N i ) + SP D t s ) = PV Security Discounting + SP D t s ). 2) In the case of a FRN a third curve is used: the forward curve related to the relevant Ibor. The three curves are: 1. Discounting risk free) : P D t). 2. Credit issuer): P C t). 3. Ibor forward): P I t). 4
9 The coupons and notional are discounted with the credit curve. The coupons are estiated with the forward curve. The approach is based on an independence hypothesis between the issuer credit risk and Ibor rates. The forward estiation is Fi I = 1 P I ) s i ) δi I P I e i ) 1. 3) The present value is PV Discounting = δ i Ni c Fi I + s c i)p C t c i) + n c 6 Clean and dirty price n N N N i P C t N i ) + SP D t s ). 4) The stander prices clean and dirty) are defined only for the bonds with unique notional payent N at the end bullet bonds). 6.1 Dirty price of a bond security fro curves The dirty price is the relative price to be paid in a fair transaction at the standard settleent date. The dirty price, denoted Dirty, should be such that PV Discounting = 0 for S = N Dirty, with t S the standard settleent date. We obtain for the dirty price Dirty Discounting = PV Security Discounting /P D t S )/N. 6.2 Fixed coupon bond present value fro clean price The present value fro the clean price is approxiately the clean price plus accrued interest ultiplied by the notional. This is not exact as it does not take into account the discounting between settleent and today and any coupon that ay be due in between. We start with the price for a bond with standard settleent date. The settleent date is denoted t 0 and the present value of a synthetic transaction with standard settleent date is denoted P Standard. Its present value is PV Standard Price = P Quoted + A)NP C t 0 ). For the coupon that are added or subtracted fro the standard one, we use the curves 7 Yield PV Transaction Price = PV Transaction Discounting PV Standard Discounting) + PV Standard Price. The yield of a bond security is a conventional nuber representing the internal rate of return of standardised cash flows. Standardised eans in this context that the exact payent dates are not taken into account but only the nuber of periods. The accrual factor fro the standard settleent date to the next coupon is denoted w. The factor is coputed using the day count convention of the bond. The yield is written only for the bonds with unique notional payent N at the end bullet bonds). 5
10 7.1 Siple interest in last period Soe bonds use a different calculation ethod in the last coupon period. The ost used ethod is the siple interest in last period or US arket final period convention. In the final period n c = 1), the siple yield is used. The dirty price at standard settleent date) is related to the yield by N Dirty = 1 + w y ) 1 cnc + N). 7.2 Copound interest in last period In the final period n c = 1), the copound interest is used. The dirty price at standard settleent date) is related to the yield by N Dirty = 1 + y ) w cnc + N). 7.3 US Street convention The US street convention assues that yield are copounded over the bond coupon period usually seiannually in US), including in the fractional first period. The dirty price at standard settleent date) is related to the yield by N Dirty = 1 + y ) w n c c i ) 1 + y i 1 + N 1 + y ) nc 1 In the final coupon period, the US arket final period convention is used. ) 7.4 UK: DMO ethod The ethod is siilar to the US street convention except that the final period uses the sae convention and not the US arket final period convention. It can be different if the first period is long or short or if there is an exdividend period. Let v = 1 + y/) 1. The coupons are all identical fro the third one: c i = c/ for i = 3,..., n c. The forula described by DMO in Debt Manageent Office 2005) is NDirty = v w c 1 + c 2 v + cv 2 ) 1 c vn 2 ) + Nv nc 1 1 v) where c 1 is the cashflow on the next date ay be 0 in the exdividend period or if the gilt has long first dividend period) and c 2 is the cash flow due on the next but one quasicoupon date ay be greater than c/ for long first dividend periods). In the last period the forula reduces to N Dirty = v w c 1 + N) and is not replaced by the siple yield approach. 6
11 7.5 US Treasury Convention The US Treasury convention assues that yields are copounded over the bond coupon period usually seiannually in US), except in the fractional first period where a siple yield is used. The dirty price at standard settleent date) is related to the yield by N Dirty = 1 + w y ) 1 n c ) c i N ) 1 + y i 1 + ) 1 + y nc 1 In the final coupon period, the US arket final period convention is used. It appears that this convention is no longer coonly used. 7.6 FRANCE:COMPND METH It is the sae ethod as the UK: DMO ethod with copound interest in the last period. 7.7 GERMAN BONDS It is the sae ethod as the US Street convention with siple interest in the last period. 7.8 Sovereign bonds conventions The following countries use the US Street convention: Spain United States The following countries use the UK: DMO ethod: United Kingdo 8 Duration and convexity 8.1 Modified duration The odified duration is a dirty) price sensitivity easure. It is the relative derivative of the price with respect to the conventional yield, i.e. Duration Modified = y Dirty y 1 + y = Duration Modified Dirty. For the US street convention and UK DMO convention it is n c c i i 1 + w ) i 1+w + For the siple interest in the last period it is Duration Modified = 1 + y N ) nc 1+w ) n 1 + w 1 N Dirty. 5) 1 + w y ) 1 w. 6) 7
12 For the copound interest in the last period it is Duration Modified = 1 + y ) 1 w. 7) The odified duration is not scaled by the notional/quantity of bonds. 8.2 Macaulay duration Macaulay duration, naed for Frederick Macaulay, who introduced the concept, is the weighted average aturity of cash flows. The discounting and the tie to aturity are in line with those of the yield convention. For US street not in the last period and DMO ethods it is coputed as Duration Macauley = n c c i i 1 + w) ) 1 + y i+w + For siple interest in the last period it is 1 + y N ) n c 1+w ) n c + w) 1 N Dirty. 8) Duration Macauley = w. 9) For US Street not in the last period and DMO ethods, the relationship between the two durations is Duration Modified = y Duration Macauley. For US Street in the last period the relationship is 1 Duration Modified = 1 + w y Duration Macauley. The Macaulay duration is not scaled by the notional/quantity of bonds. 8.3 Convexity The convexity is the relative second order derivative of the price with respect to the conventional yield, i.e. Dirty = Convexity Dirty. y For US street not in the last period and DMO ethods is coputed as Convexity = n c c i 1 + y i 1 + w) i + w) ) i+w+1 + N 1 + y For US Street in the last period the relation it is ) nc +w+1 n c 1 + w) ) n c + w) 1 N Dirty. 10) Convexity = w y ) 2 w ) 2. 11) The convexity is not scaled by the notional/quantity of bonds. 8
13 9 Other easures 9.1 Zspread The zspread is the constant spread for which the present value fro a curve plus the spread atches a present value. The spread is in the convention in which the curve is stored; this convention is usually ACT/ACT, continuously copounded. The discounting curve for a spread s and an initial curve P t) is P t) exp st). The zspread is not scaled by the notional/quantity of bonds. The coputation of the Zspread depends on the way the present value is coputed. The ost used approach is to copute the present value fro the arket quoted price as described in Section6.2. This eans that one needs a arket price, a risk free repo) curve and a issuer curve to copute the present value and the initial curve fro which the spread is coputed. The requireent is thus one price and three curves to obtain the Zspread. 9.2 Zspread sensitivity This is the present value sensitivity to the zspread. It is the parallel in the curve convention) curve sensitivity at the curve plus spread level. The zspread sensitivity is scaled by the notional/quantity of bonds. 10 Ipleentation In OGAnalytics, the bond security figures are coputed in the class BondSecurityDiscountingMethod and BondTransactionDiscountingMethod. In the Analytics viewer, the different settings can be changes through the following Properties: 1. RiskFree: the risk free/repo curve 2. Credit: the issuer specific curve 3. Curve: the base curve in particular for Zspread) 4. CalculationMethod: to change the calculation ethod. The possible values are FroCurves, FroCleanPrice, and FroYield. References Debt Manageent Office 2005). Forulae for calculating Gilt prices fro yields. Technical report, Debt Manageent Office. 3rd edition: 16 March ICMA. ICMA s rules and recoandations. rule 251 accured interest calculation. Available at and a/pdf/icmarule251.pdf. 2 9
14 placeholder
15 OpenGaa Analytics Docuentation 1. The Analytic Fraework for Iplying Yield Curves fro Market Data. 2. Multiple Curve Construction. 3. Option Pricing with Fourier Methods. 4. Bill Pricing. 5. Bond Pricing. 6. Interest Rate Futures and their Options: Soe Pricing Approaches. 7. Bond Futures: Description and Pricing. 8. Forex Options Vanilla and Sile. 9. Forex Options Digital. 10. Swaption Pricing. 11. Sile Extrapolation. 12. Inflation Instruents: ZeroCoupon Swaps and Bonds. 13. HullWhite one factor odel. 14. Swap and Cap/Floors with Fixing in Arrears or Payent Delay. 15. Replication Pricing for Linear and TEC Forat CMS. 16. Binoral With Correlation by Strike Approach to CMS Spread Pricing. 17. Libor Market Model with displaced diffusion: ipleentation. 18. Portfolio hedging with reference securities. 19. Copounded Swaps in MultiCurves Fraework 20. Curve Calibration in Practice: Requireents and NicetoHaves.
16 About OpenGaa OpenGaa helps financial services firs unify their calculation of analytics across the traditional trading and risk anageent boundaries. The copany's flagship product, the OpenGaa Platfor, is a transparent syste for frontoffice and risk calculations for financial services firs. It cobines data anageent, a declarative calculation engine, and analytics in one coprehensive solution. OpenGaa also develops a odern, independentlywritten quantitative finance library that can be used either as part of the Platfor, or separately in its own right. Released under the open source Apache License 2.0, the OpenGaa Platfor covers a range of asset classes and provides a coprehensive set of analytic easures and nuerical techniques. Find out ore about OpenGaa Download the OpenGaa Platfor developers.opengaa.co/downloads Europe OpenGaa 185 Park Street London SE1 9BL United Kingdo North Aerica OpenGaa 280 Park Avenue 27th Floor West New York, NY United States of Aerica
Example: Suppose that we deposit $1000 in a bank account offering 3% interest, compounded monthly. How will our money grow?
Finance 111 Finance We have to work with oney every day. While balancing your checkbook or calculating your onthly expenditures on espresso requires only arithetic, when we start saving, planning for retireent,
More informationFixedIncome Securities and Interest Rates
Chapter 2 FixedIncoe Securities and Interest Rates We now begin a systeatic study of fixedincoe securities and interest rates. The literal definition of a fixedincoe security is a financial instruent
More information1 Interest rates and bonds
1 Interest rates and bonds 1.1 Copounding There are different ways of easuring interest rates Exaple 1 The interest rate on a oneyear deposit is 10% per annu. This stateent eans different things depending
More informationPERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO
Bulletin of the Transilvania University of Braşov Series I: Engineering Sciences Vol. 4 (53) No.  0 PERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO V. CAZACU I. SZÉKELY F. SANDU 3 T. BĂLAN Abstract:
More informationInvesting in corporate bonds?
Investing in corporate bonds? This independent guide fro the Australian Securities and Investents Coission (ASIC) can help you look past the return and assess the risks of corporate bonds. If you re thinking
More informationInvesting in corporate bonds?
Investing in corporate bonds? This independent guide fro the Australian Securities and Investents Coission (ASIC) can help you look past the return and assess the risks of corporate bonds. If you re thinking
More informationAnalysis of the purchase option of computers
Analysis of the of coputers N. Ahituv and I. Borovits Faculty of Manageent, The Leon Recanati Graduate School of Business Adinistration, TelAviv University, University Capus, RaatAviv, TelAviv, Israel
More informationInterest Rate and Currency Swaps
Interest Rate and Currency Swaps Eiteman et al., Chapter 14 Winter 2004 Bond Basics Consider the following: ZeroCoupon ZeroCoupon OneYear Implied Maturity Bond Yield Bond Price Forward Rate t r 0 (0,t)
More informationUse of extrapolation to forecast the working capital in the mechanical engineering companies
ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL 2014. Vol. 1. No. 1. 23 28 Use of extrapolation to forecast the working capital in the echanical engineering copanies A. Cherep, Y. Shvets Departent of finance
More informationESTIMATING LIQUIDITY PREMIA IN THE SPANISH GOVERNMENT SECURITIES MARKET
ESTIMATING LIQUIDITY PREMIA IN THE SPANISH GOVERNMENT SECURITIES MARKET Francisco Alonso, Roberto Blanco, Ana del Río and Alicia Sanchis Banco de España Banco de España Servicio de Estudios Docuento de
More informationQuality evaluation of the modelbased forecasts of implied volatility index
Quality evaluation of the odelbased forecasts of iplied volatility index Katarzyna Łęczycka 1 Abstract Influence of volatility on financial arket forecasts is very high. It appears as a specific factor
More informationF3 Financial Strategy. Examiner s Answers
Strategic Level Paper F3 Financial Strategy March 2014 exaination Exainer s Answers Question One Rationale Question One focusses on an external party a hotel chain, which is hoping to set up a hotel in
More informationIntroduction to Fixed Income (IFI) Course Syllabus
Introduction to Fixed Income (IFI) Course Syllabus 1. Fixed income markets 1.1 Understand the function of fixed income markets 1.2 Know the main fixed income market products: Loans Bonds Money market instruments
More informationOpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem
OpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem Marc Henrard marc@opengamma.com OpenGamma Quantitative Research n. 1 November 2011 Abstract
More informationACI THE FINANCIAL MARKETS ASSOCIATION
ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARDFORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE
More informationCashsettled swaptions How wrong are we?
Cashsettled swaptions How wrong are we? Marc Henrard Quantitative Research  OpenGamma 7th Fixed Income Conference, Berlin, 7 October 2011 ... Based on: Cashsettled swaptions: How wrong are we? Available
More informationSWAPTION PRICING OPENGAMMA QUANTITATIVE RESEARCH
SWAPTION PRICING OPENGAMMA QUANTITATIVE RESEARCH Abstract. Implementation details for the pricing of European swaptions in different frameworks are presented.. Introduction This note describes the pricing
More informationConstruction Economics & Finance. Module 3 Lecture1
Depreciation: Construction Econoics & Finance Module 3 Lecture It represents the reduction in arket value of an asset due to age, wear and tear and obsolescence. The physical deterioration of the asset
More informationTIME VALUE OF MONEY PROBLEMS CHAPTERS THREE TO TEN
TIME VLUE OF MONEY PROBLEMS CHPTERS THREE TO TEN Probles In how any years $ will becoe $265 if = %? 265 ln n 933844 9 34 years ln( 2 In how any years will an aount double if = 76%? ln 2 n 9 46 years ln76
More informationResearch Article Performance Evaluation of Human Resource Outsourcing in Food Processing Enterprises
Advance Journal of Food Science and Technology 9(2): 964969, 205 ISSN: 20424868; eissn: 20424876 205 Maxwell Scientific Publication Corp. Subitted: August 0, 205 Accepted: Septeber 3, 205 Published:
More informationSWAP AND CAP/FLOORS WITH FIXING IN ARREARS OR PAYMENT DELAY
SWAP AND CAP/FLOORS WITH FIXING IN ARREARS OR PAYMENT DELAY OPENGAMMA QUANTITATIVE RESEARCH Abstract. Pricing methods for swaps and caps/floors with fixing in arrears or payment delays are proposed. The
More informationDependent Events and Operational Risk
Dependent Events and Operational Risk Miro R. Powojowski, Diane Reynolds and Hans J.H. Tuenter Most people acknowledge that soe correlation between operational losses exists. Modelling it, however, is
More informationMONEY MARKET SUBCOMMITEE(MMS) FLOATING RATE NOTE PRICING SPECIFICATION
MONEY MARKET SUBCOMMITEE(MMS) FLOATING RATE NOTE PRICING SPECIFICATION This document outlines the use of the margin discounting methodology to price vanilla money market floating rate notes as endorsed
More information 265  Part C. Property and Casualty Insurance Companies
Part C. Property and Casualty Insurance Copanies This Part discusses proposals to curtail favorable tax rules for property and casualty ("P&C") insurance copanies. The syste of reserves for unpaid losses
More informationLecture 09: Multiperiod Model Fixed Income, Futures, Swaps
Lecture 09: Multiperiod Model Fixed Income, Futures, Swaps Prof. Markus K. Brunnermeier Slide 091 Overview 1. Bond basics 2. Duration 3. Term structure of the real interest rate 4. Forwards and futures
More informationADJUSTING FOR QUALITY CHANGE
ADJUSTING FOR QUALITY CHANGE 7 Introduction 7.1 The easureent of changes in the level of consuer prices is coplicated by the appearance and disappearance of new and old goods and services, as well as changes
More informationEquityindexlinked swaps
Equityindexlinked swaps Equivalent to portfolios of forward contracts calling for the exchange of cash flows based on two different investment rates: a variable debt rate (e.g. 3month LIBOR) and the
More informationFuzzy Sets in HR Management
Acta Polytechnica Hungarica Vol. 8, No. 3, 2011 Fuzzy Sets in HR Manageent Blanka Zeková AXIOM SW, s.r.o., 760 01 Zlín, Czech Republic blanka.zekova@sezna.cz Jana Talašová Faculty of Science, Palacký Univerzity,
More informationChapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixedincome securities. Stocks. Real assets (capital budgeting). Part C Determination
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More informationFIXEDINCOME SECURITIES. Chapter 11. Forwards and Futures
FIXEDINCOME SECURITIES Chapter 11 Forwards and Futures Outline Futures and Forwards Types of Contracts Trading Mechanics Trading Strategies Futures Pricing Uses of Futures Futures and Forwards Forward
More informationThe United States was in the midst of a
A Prier on the Mortgage Market and Mortgage Finance Daniel J. McDonald and Daniel L. Thornton This article is a prier on ortgage finance. It discusses the basics of the ortgage arket and ortgage finance.
More informationA framework for performance monitoring, load balancing, adaptive timeouts and quality of service in digital libraries
Int J Digit Libr (2000) 3: 9 35 INTERNATIONAL JOURNAL ON Digital Libraries SpringerVerlag 2000 A fraework for perforance onitoring, load balancing, adaptive tieouts and quality of service in digital libraries
More informationTrading the Yield Curve. Copyright 19992006 Investment Analytics
Trading the Yield Curve Copyright 19992006 Investment Analytics 1 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading
More informationAnalytical Research Series
EUROPEAN FIXED INCOME RESEARCH Analytical Research Series INTRODUCTION TO ASSET SWAPS Dominic O Kane January 2000 Lehman Brothers International (Europe) Pub Code 403 Summary An asset swap is a synthetic
More informationEvaluating Inventory Management Performance: a Preliminary DeskSimulation Study Based on IOC Model
Evaluating Inventory Manageent Perforance: a Preliinary DeskSiulation Study Based on IOC Model Flora Bernardel, Roberto Panizzolo, and Davide Martinazzo Abstract The focus of this study is on preliinary
More informationSwapEx Contract Specifications. USD LIBOR Interest Rate Swaps: FixedtoFloating
SwapEx Contract Specifications USD LIBOR Interest Rate Swaps: FixedtoFloating There are two types of USD LIBOR Interest Rate Swaps; FixedtoFloating contracts available for trading on SwapEx: Fixed Rate
More informationIntroduction to swaps
Introduction to swaps Steven C. Mann M.J. Neeley School of Business Texas Christian University incorporating ideas from Teaching interest rate and currency swaps" by Keith C. Brown (TexasAustin) and Donald
More informationHW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:
HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exa FM/CAS Exa 2. Chapter 1. Basic Interest Theory. c 2008. Miguel A. Arcones. All rights reserved. Extract fro: Arcones Manual for the SOA Exa FM/CAS Exa 2, Financial Matheatics. Spring
More informationRisk and Investment Conference 2013. Brighton, 17 19 June
Risk and Investment Conference 03 Brighton, 7 9 June 0 June 03 Acquiring fixed income assets on a forward basis Dick Rae, HSBC and Neil Snyman, Aviva Investors 8 June 0 Structure of Presentation Introduction
More information550.444 Introduction to Financial Derivatives
550.444 Introduction to Financial Derivatives Week of October 7, 2013 Interest Rate Futures Where we are Last week: Forward & Futures Prices/Value (Chapter 5, OFOD) This week: Interest Rate Futures (Chapter
More informationThe public private partnership paradox
The public private partnership paradox Stephen Gray * UQ Business School, University of Queensland Jason Hall UQ Business School, University of Queensland Grant Pollard Value Decisions ABSTRACT A public
More informationFIXEDINCOME SECURITIES. Chapter 10. Swaps
FIXEDINCOME SECURITIES Chapter 10 Swaps Outline Terminology Convention Quotation Uses of Swaps Pricing of Swaps Non Plain Vanilla Swaps Terminology Definition Agreement between two parties They exchange
More informationProject Evaluation Roadmap. Capital Budgeting Process. Capital Expenditure. Major Cash Flow Components. Cash Flows... COMM2501 Financial Management
COMM501 Financial Manageent Project Evaluation 1 (Capital Budgeting) Project Evaluation Roadap COMM501 Financial Manageent Week 7 Week 7 Project dependencies Net present value ethod Relevant cash flows
More informationOnline Appendix I: A Model of Household Bargaining with Violence. In this appendix I develop a simple model of household bargaining that
Online Appendix I: A Model of Household Bargaining ith Violence In this appendix I develop a siple odel of household bargaining that incorporates violence and shos under hat assuptions an increase in oen
More informationASSET LIABILITY MANAGEMENT Significance and Basic Methods. Dr Philip Symes. Philip Symes, 2006
1 ASSET LIABILITY MANAGEMENT Significance and Basic Methods Dr Philip Symes Introduction 2 Asset liability management (ALM) is the management of financial assets by a company to make returns. ALM is necessary
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationBOND FUTURES. 1. Terminology... 2 2. Application... 11. FINANCE TRAINER International Bond Futures / Page 1 of 12
BOND FUTURES 1. Terminology... 2 2. Application... 11 FINANCE TRAINER International Bond Futures / Page 1 of 12 1. Terminology A future is a contract to either sell or buy a certain underlying on a specified
More informationCHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
More informationSUPPORTING YOUR HIPAA COMPLIANCE EFFORTS
WHITE PAPER SUPPORTING YOUR HIPAA COMPLIANCE EFFORTS Quanti Solutions. Advancing HIM through Innovation HEALTHCARE SUPPORTING YOUR HIPAA COMPLIANCE EFFORTS Quanti Solutions. Advancing HIM through Innovation
More informationINTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 4. Convexity and CMS Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York February 20, 2013 2 Interest Rates & FX Models Contents 1 Introduction
More informationSmall Business ebook. 5 Steps to a killer social media strategy
Sall Business ebook 5 Steps to a killer social edia strategy About the authors John Keepax and Frank Irias offer ore than 32 years of cobined experience in the areas of John Keepax Creative Director /
More informationAdvanced forms of currency swaps
Advanced forms of currency swaps Basis swaps Basis swaps involve swapping one floating index rate for another. Banks may need to use basis swaps to arrange a currency swap for the customers. Example A
More informationDIGITAL FOREX OPTIONS
DIGITAL FOREX OPTIONS OPENGAMMA QUANTITATIVE RESEARCH Abstract. Some pricing methods for forex digital options are described. The price in the GarhmanKohlhagen model is first described, more for completeness
More informationarxiv:0805.1434v1 [math.pr] 9 May 2008
Degreedistribution stability of scalefree networs Zhenting Hou, Xiangxing Kong, Dinghua Shi,2, and Guanrong Chen 3 School of Matheatics, Central South University, Changsha 40083, China 2 Departent of
More informationSOME APPLICATIONS OF FORECASTING Prof. Thomas B. Fomby Department of Economics Southern Methodist University May 2008
SOME APPLCATONS OF FORECASTNG Prof. Thoas B. Foby Departent of Econoics Southern Methodist University May 8 To deonstrate the usefulness of forecasting ethods this note discusses four applications of forecasting
More informationAn Improved Decisionmaking Model of Human Resource Outsourcing Based on Internet Collaboration
International Journal of Hybrid Inforation Technology, pp. 339350 http://dx.doi.org/10.14257/hit.2016.9.4.28 An Iproved Decisionaking Model of Huan Resource Outsourcing Based on Internet Collaboration
More informationVALUATION OF PLAIN VANILLA INTEREST RATES SWAPS
Graduate School of Business Administration University of Virginia VALUATION OF PLAIN VANILLA INTEREST RATES SWAPS Interestrate swaps have grown tremendously over the last 10 years. With this development,
More informationThe Irony In The Derivatives Discounting
The Irony In The Derivatives Discounting Marc Henrard Head of Quantitative Research, Banking Department, Bank for International Settlements, CH4002 Basel (Switzerland), email: Marc.Henrard@bis.org Abstract
More informationExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona Network
2013 European Control Conference (ECC) July 1719, 2013, Zürich, Switzerland. ExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona
More informationThe Research of Measuring Approach and Energy Efficiency for Hadoop Periodic Jobs
Send Orders for Reprints to reprints@benthascience.ae 206 The Open Fuels & Energy Science Journal, 2015, 8, 206210 Open Access The Research of Measuring Approach and Energy Efficiency for Hadoop Periodic
More informationDerivatives Interest Rate Futures. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles
Derivatives Interest Rate Futures Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Interest Rate Derivatives Forward rate agreement (FRA): OTC contract
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More informationFixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
More informationPhysics 211: Lab Oscillations. Simple Harmonic Motion.
Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.
More informationLearning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002
Learning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002 Aaron Nematnejad works in the fixed income analytics team at Bloomberg L.P. in London. He graduated
More informationIntroduction to Unit Conversion: the SI
The Matheatics 11 Copetency Test Introduction to Unit Conversion: the SI In this the next docuent in this series is presented illustrated an effective reliable approach to carryin out unit conversions
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationAssumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk
Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,
More informationHot Topics in Financial Markets Lecture 1: The Libor Scandal
Hot Topics in Financial Markets Lecture 1: The Libor Scandal Spot and Forward Interest Rates Libor LiborDependent Financial Instruments The Scandal 2 Spot Interest Rates Bond Market The yield on a bond
More informationCalculating the Return on Investment (ROI) for DMSMS Management. The Problem with Cost Avoidance
Calculating the Return on nvestent () for DMSMS Manageent Peter Sandborn CALCE, Departent of Mechanical Engineering (31) 453167 sandborn@calce.ud.edu www.ene.ud.edu/escml/obsolescence.ht October 28, 21
More informationOption B: Credit Card Processing
Attachent B Option B: Credit Card Processing Request for Proposal Nuber 4404 Z1 Bidders are required coplete all fors provided in this attachent if bidding on Option B: Credit Card Processing. Note: If
More informationDanske Bank acquires Sampo Bank
Danske Bank acquires Sapo Bank Overview of Sapo Bank Noveber 9, 2006 Disclaier This presentation is not for release, publication or distribution in Australia, Canada, the Hong Kong Special Adinistrative
More informationThis paper studies a rental firm that offers reusable products to price and qualityofservice sensitive
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol., No. 3, Suer 28, pp. 429 447 issn 523464 eissn 5265498 8 3 429 infors doi.287/so.7.8 28 INFORMS INFORMS holds copyright to this article and distributed
More informationTreasury Floating Rate Notes
Global Banking and Markets Treasury Floating Rate Notes DATE: April 2012 Recommendation summary The USD 7trn money market should support significant FRN issuance from the Treasury. This would diversify
More informationCRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS
641 CRM FACTORS ASSESSMENT USING ANALYTIC HIERARCHY PROCESS Marketa Zajarosova 1* *Ph.D. VSB  Technical University of Ostrava, THE CZECH REPUBLIC arketa.zajarosova@vsb.cz Abstract Custoer relationship
More informationTreasury Bond Futures
Treasury Bond Futures Concepts and Buzzwords Basic Futures Contract Futures vs. Forward Delivery Options Reading Veronesi, Chapters 6 and 11 Tuckman, Chapter 14 Underlying asset, markingtomarket, convergence
More informationInterest Rate Swaps. Key Concepts and Buzzwords. Readings Tuckman, Chapter 18. Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps
Interest Rate Swaps Key Concepts and Buzzwords Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps Readings Tuckman, Chapter 18. Counterparty, Notional amount, Plain vanilla swap, Swap rate Interest
More informationAnalyzing Spatiotemporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy
Vol. 9, No. 5 (2016), pp.303312 http://dx.doi.org/10.14257/ijgdc.2016.9.5.26 Analyzing Spatioteporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy Chen Yang, Renjie Zhou
More informationStudy on the development of statistical data on the European security technological and industrial base
Study on the developent of statistical data on the European security technological and industrial base Security Sector Survey Analysis: France Client: European Coission DG Migration and Hoe Affairs Brussels,
More informationEXP 481  Capital Markets Option Pricing. Options: Definitions. Arbitrage Restrictions on Call Prices. Arbitrage Restrictions on Call Prices 1) C > 0
EXP 481  Capital Markets Option Pricing imple arbitrage relations Payoffs to call options Blackcholes model PutCall Parity Implied Volatility Options: Definitions A call option gives the buyer the
More informationINSTITUTE AND FACULTY OF ACTUARIES EXAMINATION
INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 14 April 2016 (pm) Subject ST6 Finance and Investment Specialist Technical B Time allowed: Three hours 1. Enter all the candidate and examination details
More informationMachine Learning Applications in Grid Computing
Machine Learning Applications in Grid Coputing George Cybenko, Guofei Jiang and Daniel Bilar Thayer School of Engineering Dartouth College Hanover, NH 03755, USA gvc@dartouth.edu, guofei.jiang@dartouth.edu
More informationThe new ACI Diploma. Unit 2 Fixed Income & Money Markets. Effective October 2014
The new ACI Diploma Unit 2 Fixed Income & Money Markets Effective October 2014 8 Rue du Mail, 75002 Paris  France T: +33 1 42975115  F: +33 1 42975116  www.aciforex.org The new ACI Diploma Objective
More informationn(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3
ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric
More informationPricing Asian Options using Monte Carlo Methods
U.U.D.M. Project Report 9:7 Pricing Asian Options using Monte Carlo Methods Hongbin Zhang Exaensarbete i ateatik, 3 hp Handledare och exainator: Johan Tysk Juni 9 Departent of Matheatics Uppsala University
More informationGraphing Exponential Functions
Graphing Eponential Functions Another coonly used type of nonlinear function is the eponential function. We focus in this section on eponential graphs and solving equations. Another section is loaded
More informationInvention of NFV Technique and Its Relationship with NPV
International Journal of Innovation and Applied Studies ISSN 20289324 Vol. 9 No. 3 Nov. 2014, pp. 11881195 2014 Innovative Space of Scientific Research Journals http://www.ijias.issrjournals.org/ Invention
More informationFixed Income, Zero coupon rates and Duration
Chapter 5 Fixed Income, Zero coupon rates and Duration Fixedincome securities are tradable debt notes issued by an organization in which it declares that it will repay a borrowed amount with interest
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationFinance 350: Problem Set 6 Alternative Solutions
Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas
More information2015 Exam 2 Syllabus Financial Mathematics Exam
2015 Exam 2 Syllabus Financial Mathematics Exam The syllabus for this exam is defined in the form of learning objectives that set forth, usually in broad terms, what the candidate should be able to do
More informationLearning Curve Interest Rate Futures Contracts Moorad Choudhry
Learning Curve Interest Rate Futures Contracts Moorad Choudhry YieldCurve.com 2004 Page 1 The market in shortterm interest rate derivatives is a large and liquid one, and the instruments involved are
More information2 Stock Price. Figure S1.1 Profit from long position in Problem 1.13
Problem 1.11. A cattle farmer expects to have 12, pounds of live cattle to sell in three months. The livecattle futures contract on the Chicago Mercantile Exchange is for the delivery of 4, pounds of cattle.
More informationCallable Bonds  Structure
1.1 Callable bonds A callable bond is a fixed rate bond where the issuer has the right but not the obligation to repay the face value of the security at a preagreed value prior to the final original maturity
More informationCHAPTER 20. Financial Options. Chapter Synopsis
CHAPTER 20 Financial Options Chapter Synopsis 20.1 Option Basics A financial option gives its owner the right, but not the obligation, to buy or sell a financial asset at a fixed price on or until a specified
More informationLearning Curve Using Bond Futures Contracts for Trading and Hedging Moorad Choudhry
Learning Curve Using Bond Futures Contracts for Trading and Hedging Moorad Choudhry YieldCurve.com 2004 Page 1 A widely used risk management instrument in the debt capital markets is the government bond
More informationInvestment and Portfolio Management. Lecture 8 Bond Prices and Yields. Bond Characteristics
Investment and Portfolio Management Ms. Pham Le Thu Nga Lecture 8 Bond Prices and Yields Chapter 14 142 Bond Characteristics Face or par value (normally bullet maturity) Coupon rate (normally fixed) Zero
More information