?_J`:1lpJE ( 4 .1   & MathType-C@)Times New Roman-!DP!VP !VkU!V@Symbol-!=P!-P !-P\ !+k!k !n Symbol-!-PTimes New Roman+-!(P!)P !(P!)k!(k!)P_!10P/ !10k!0k !20k !10 Times New Roman-!4PTimes New Roman+-! bpP! bp "System-/&;)z4tvG~ g |CONTEXT{|CTXOMAPo|FONTn|KWBTREEr|KWDATAq|KWMAP r|SYSTEM/ |TOPIC |TTLBTREELz|bm0|bm1|bm2y|bm3 'lpD  .1   & MathType-ER@)Times New RomanX-!Df!VP\!dVf!dr@Symbol-!=@!-PTimes New RomanX-!1 "System-lpE@ G .1   & MathType-! Times New Roman-!C!V8!d!Vh!drSymbol-!=Times New Roman-!12Times New Roman-!2 !2 "System-l-AKA Valuation Primer HelpICreateButton("QuickHelp", "&?", "PopupId(`primer.hlp', `HC_QUICKHELP')")BrowseButtons()F`=` NZ1ZAKA Valuation Primer Contentsh, < HZB%["AKA Valuation Primer Help Contents `;Z"% vRWelcome to the Help system for the AKA Valuation Primer.s FoRG em eC2 eRЀ Ү ㅉ;ր JumpContents("faj.hlp")  Yield Curve Models menu Valuation menu Duration menu Refunding menu Help menu Andrew Kalotay Associates The FAJ Article H"1[wYield Curve Models menuh,E< HZB%["AKA Valuation Primer Help Contents `;% vRWelcome to the Help system for the AKA Valuation Primer.OE0 0>R`rU Yield Curve Models menug*[= JTZRR) Ym >Z6 Zero VolatilityBinomial Processw RemeC2 eRЀҮㅉ;րJumpContents("faj.hlp")  Valuation menu Duration menu Refunding menu Help menu Andrew Kalotay Associates The FAJ Article ?[1EValuation menuh,w< HZB%["AKA Valuation Primer Help Contents `;~% vRWelcome to the Help system for the AKA Valuation Primer.q4= JhRG`rU Yield Curve Models menu Valuation menuS~B TZRRE%׀H֔@=TFCertain CashflowsCertain Option PayoutsOptionless BondsCallable Bonds@. ,$^RPBPutable Bondsu րReC2 eRЀҮㅉ;րJumpContents("faj.hlp")  Duration menu Refunding menu Help menu Andrew Kalotay Associates The FAJ Article > 1 [ Duration menuh,b < HZB%["AKA Valuation Primer Help Contents `; % vRWelcome to the Help system for the AKA Valuation Primer.Kb ] P pRGem `rU Yield Curve Models menu Valuation menu Duration menuZ& 4 8LZRRFH8ViOptionless BondsCallable Bonds@] . ,$^RP㍻LPutable Bonds^ p ReRЀҮㅉ;րJumpContents("faj.hlp")  Refunding menu Help menu Andrew Kalotay Associates The FAJ Article ?  1A Refunding Menuh, l < HZB%["AKA Valuation Primer Help Contents `; % vRWelcome to the Help system for the AKA Valuation Primer.`l ] RGemeC2 `rU Yield Curve Models menu Valuation menu Duration menu Refunding menu7 - *ZRR`TCalls: . ,^RP]|ȗTendersI c RҮㅉ;րJumpContents("faj.hlp")  Help menu Andrew Kalotay Associates The FAJ Article : 1=wAHelp Menuh,H< HZB%["AKA Valuation Primer Help Contents `;% vRWelcome to the Help system for the AKA Valuation Primer.pH@j RGemeC2 eRЀ@`rU Yield Curve Models menu Valuation menu Duration menu Refunding menu Help menu4(Af hZRR Search()ioG HelpOn()JumpContents("faj.hlp")IndexKeyboardUsing HelpThe FAJ Article8 @`A. ,^RPSAbout9(AAV |rRㅉ;րJumpContents("faj.hlp")  Andrew Kalotay Associates The FAJ Article J`A9B1A9BDAndrew Kalotay Associatesh,AB< HZB%["AKA Valuation Primer Help Contents `;9BC% vRWelcome to the Help system for the AKA Valuation Primer.B Dx !RGemeC2 eRЀҮ`rU Yield Curve Models menu Valuation menu Duration menu Refunding menu Help menu Andrew Kalotay Associatesi.CrD; F\ZRR%[KJ#ServicesPrincipalsLicensed Productsb DDI b2RJumpContents("faj.hlp")  The FAJ Article @rDE1-EGZero VolatilityO(DcE' PBStripping the Curve: Zero VolatilityEKFJ b=R nrL* E;鉀 DcThis module explores the relationship among the par yield curve, the forward one-period rates, the zero coupon rates, and the discount factors.cEG. *R You may change any of the values on the screen. Press the ENTER key or tab to the next field to recompute the different curves. BKFCG1OCGPJThe Binomial Tree]6GG' lB The Elementary Binomial Tree with a Lognormal LimitCGH> JYR nrL* HӉThis module explores the relationship among the par yield curve, the forward one-period rates, the volatility, and a simple binomial tree with a lognormal limit.GPJ? LR   Adjacent rates at the same point in time have the constant ratio exp(2xVolatility), where the volatility is expressed in percent. The rates on the tree are then contructed so that the four bonds which make up the par yield curve are priced at par.You may change any of the values on the screen. Press the ENTER key or tab to the next field to recompute the different curves.JHJ1> JMValuing Certain CashflowsGPJJ* $:BValuing Certain CashflowsJK2 2R E;rL*Certain cashflows can be correctly valued either by discounting each flow at its own "spot" or zero coupon rate or by rolling the flows back period by period at the one-period forward rates.)JM: BR nP9 7Set up the par yield curve, and enter the terms of a bond by setting its coupon and principal cashflows. In the lower two-thirds of the screen, you will see the two methods of discounting each yield the same value for any bond. OKPM1 m PMValuing Certain Option PayoutsH!MM' BB Valuing Certain Option PayoutsPMMO2 2R ЉmrL*Certain option payouts cashflows can be correctly valued in a zero-volatility world by rolling the flows back period by period at the one-period forward rates. At each option exercise opportunity, one examines the intrinsic value of the option and its marginal time value. When the time value is zero--i.e., where there is no value to be had by waiting--the option is exercised.yMF ZR nP9 7;rL*Set up the par yield curve, and enter the terms of a callable bond by setting its coupon, principal caMOMshflows and call prices. In the lower half of the screen, you will see the forward one-period rates and the discounted cashflows. When a value appears as white on red, the option was exercised. Note how the value of the future flows exceeds the call price. U$MOm1G m+Andrew Kalotay Associates: ServicesC' 8B Andrew Kalotay Associates mЃ& R Andrew Kalotay Associates, a leading authority on the valuation of fixed income securities, offers orporate and sovereign borrowers tailored advice that brings dramatic improvement in portfolio performance. Whether restructuring debt, assessing new financial products, or honing a trading strategy, selective clients depend on our proven analytics to safeguard their balance sheets. Under our direct guidance, borrowers carried out more than seven billion dollars in primary market transactions alone.[1+* "cR Andrew Kalotay Associates' precision analytics take the guesswork out of liability management. Our dynamic system for reducing debt cost and controlling interest rate risk embraces the latest in valuation methodology. Clients continually improve performance by gauging market opportunities against the expected benefits of standing pat.Andrew Kalotay Associates provides related services to investment banks and major investors. At last financial managers have at hand an essential service that meets their particualr needs with customized strategies.W&Ѓ1< gAndrew Kalotay Associates: PrincipalsC+ņ' 8B Andrew Kalotay Associatesz??; F~R."PybSdAndrew J. KalotayGeorge O. WilliamsC. Douglas Howard(ņg% R B?17GD Andrew J. Kalotay;g' (B Andrew J. KalotayH,, &9R  Andrew J. Kalotay has over twenty years of investment banking experience during which time he has structured transactions from both the issuance and retirement sides amounting to more than sixty billion dollars. The transactions have earned him a reputation for making debt pay.l‹* "R Prior to founding the firm, Dr. Kalotay was Director - Research in the Bond Portfolio Analysis Group at Salomon brothers. Before coming to Wall Street, he was with the Treasury Department at AT&T and with Bell Laboratories. His numerous publications include an award-winning paper on the valuation and management of callable bonds.He has a Ph.D. from the University of Toronto, has taught at Wharton and the Columbia Business School, and is presently on the faculty of Fordham University. A past President of the Fixed Income Analysts Society, he is currently a Trustee of the Financial Management Association.(,% R C‹-1M) -iGeorge O. Williams<i' *B George O. Williams-\& R George O. Williams has been a frequent advisor to major institutions on the design and implementation of computer-based solutions to problems in finance. He has a Ph.D. from the State University of New York and has published widely in applied mathematics and finance. His past academic appointments include a research faculty position at New York University's Courant Institute. He is Dean of Quantitative Analysis for the Fixed Income Analysts Society. )i& R Y(\ގ1eDގ0pC. Douglas Howard: Exclusive ConsultantR+0' VB C. Douglas Howard: Exclusive Consultant ގG& R C. Douglas Howard, formerly a Vice President in the Bond Portfolio Analysis Group at Salomon Brothers, is engaged through DHAnalyticsInc. to develop the firm's analyt0Gic tools. He has unique expertise in simulation and optimization methods in finance and is the author of several seminal papers on interest rate and currency risk management. Mr. Howard has an M.B.A. in Finance from Columbia University and is currently affiliated with New York University's Courant Institute.)0p& R BG1 ) wLicensed Products=p) "(Bt Licensed ProductsE4( ;Rt Precision analytics take the guesswork out of liability management. Our dynamic system for reducing debt cost and controlling interest rate risk embraces the latest in valuation methodology. Clients continually improve performance by gauging market opportunities against the expected benefits of standing pat. Our flexible approach also factors in specific tax, accounting, and regulatory consuiderations. In short, financial managers now have at hand an essential service that meets their particular needs with customized strategies.f;+ &vRt BondVal: Option-adjusted arbitrage-free bond valuations4]P pZRVt     Pre- and after-tax valuationForward securitiesCashflowsCoupon fixingYield curve analysisd9+ &rRt SwapVal: Arbitrage-free interest-rate swap valuation`]nM jZRVt     SwapsForward swapsOptions on swapsCancelable swapsYield curve analysisk@+ &Rt PortVal: Option-adjusted arbitrage-free portfolio valuationcnE ZZRVt    Pre- and after-tax valuationMarket price analysisCashflowsYield curve analysisi>+ &|Rt FloatVal: Arbitrage-free floating-rate security valuationV zYZRVt      CMT floatersAdjustable-rate mortgagesStep-up coupon bondsIndexed amortizing notesVariable cap and floor balancesAmerican and European options[0G+ &`Rt NewBond: New issue structuring and analysistE ZZRVt    Fair coupon determinationMarket coupon analysisPre- and after-tax valuationYield curve analysisg<Gg+ &xRt BondRef: After-tax option-based bond refunding analysisPY ZRVt      Call interest-rate sensitivity and efficiency analysisTender price and interest-rate sensitivity and efficiency analysisWait-until-call breakeven analysisSinking fund repurchase analysisCashflowsYield curve analysisGg( >RtEmprical Global OptimizationyCw6 <ZR:t  Optimization against a benchmarkAsset-liability matchingD1The Par Yield Curve?w) ",Bt The Par Yield CurverMl% R The coupons paid by full-coupon bonds priced at par at each maturity. )& R R!l1AֈThe Forward One-Period Rate CurveG .' @B Forward One-Period Rate Curve8 f, &R n뉂The period-by-period sequence of forward one-period rates consistent with the par yield curve. For example, the one-period rate one period forward is that rate which makes one indifferent between a two-period security and a sequence of two one-period securities.).& R Bf1,Zero Coupon Curve;' (B Zero Coupon Curve,9 @R   DcThe set of rates appropriate for discounting a pure cashflow. When discounted at the appropriate zero-coupon rate, one dollar of cashflow k periods in the future has a value given by the k'th discount factor.Am1ֈmDiscount Factors:,' &B Discount Factors mD VR    E;鉀 The sequence of values of one dollar paid k periods in the future. Discounting one dollar for k periods at the k-period zero-coupon discount rate produces the k-period discount factor.)& R I#1#Interest Rate VolatilityBe' 6B Interest Rate Volatility*#&  R The annualized standard deviation of the logarithm of the one-period interest rate. A volatility of 10% in an annual-pay binomial world means that the short rate will be either 110% of what it is today or 90.909...% of what it is today one year from today.)e& R F15VZero Volatility World?=' 0B Zero Volatility Worldb% R A world in which rates evolve to the forward rates. All future rates are known with certainty.)=& R 7$1p$]Coupon0 T' B Coupon$4, &iR  The interest rate on the bond. We consider only annual-pay bonds here. Most real bonds pay interest semi-annually, and the coupon rate is said to be a Bond Equivalent Yield.)T]& R @41V3- Principal Flows9]' $B Principal Flows. & R The timing of the principal payments. Note that the total cashflow will be both principal and interest. The program maintains the sum of the principal flows at 100. You can play games and have negative principal flows, so long as the sum of all flows is 100.)- & R >  k 1k  Call Schedule7-  '  B Call Schedulek  & R The times and prices at which the issuer has the right to repurchase the bond prior to maturity. We consider only European options here, but most callable bonds have American call options.)  & R =  13 I Put Schedule6 $ ' B Put Schedule  & R The times and prices at which the investor has the right to force the issuer to repurchase the bond prior to maturity. We consider only European options here, which is the way most putable bonds are structured.)$ I & R I  1>   Valuing Optionless BondsBI  ' 6B Valuing Optionless Bonds(  % R G C 1(C  Valuing Callable Bonds@  ' 2B Valuing Callable Bonds(C  % R F  1  XValuing Putable Bonds? 0' 0B Valuing Putable Bonds( X% R N01DDuration for Optionless BondsG X' @B Duration for Optionless Bonds  @, &R  The goal of duration is to quantify the change in a bond's price for a given change in interest rates. The effective duration of a bond is defined as the percent change in price divided by the change in interest rates. @X4BQ pkR    "  Numerically, this is computed by shifting the yield curve in parallel fashion up and down, say, ten basis points. The bond is priced in each of these environments and in the original, unshifted environment, producing respective values V(+10bp), V(-10bp), and V(0). The duration is thenwhere the order of the terms in the numerator has been chosen to produce a positive quantity for ordinary bonds. Note that since interest rates are generally quoted per annum, the units of duration are years. More formally, the duration may be expressed as @DE XR "   For optionless bonds, this quantity is nearly the same as the archaic measure known as the modified duration, which is computed not from changes in interest rates but from changes in the yield to maturity. This quantity and the related Macaulay duration should not be used.The duration is only a linear approximation to the price sensitivity of a security. A higher-order correction is provided by the convexity, which is formally expressed as5BD0 0 R "LD!E1C$!EfEDuration for Callable BondsEDfE' <B Duration for Callable BondsK!EE1 EEDuration for Putable BondsDfEE' :B Duration for Putable BondsFE;F1\!;FFCall Efficiency Study?EzF' 0B Call Efficiency Study(;FF% R HzFF1A"FSGTender Efficiency StudyAF+G' 4B Tender Efficiency Study(FSG% R 6+GG1#GIAbout/SGG' B AboutjGMH+ &R This menu selection displays an About dialog box that tells how to contact Andrew Kalotay Associates.)GvH& R ZMHIG ^R ㅉ;։%[KJ#See also:Andrew Kalotay AssociatesServicesPrincipalsLicensed ProductsCvHZI1[$ZIrMQuick Help on Help<II' *B Quick Help on Helpc8ZII+ &pR  For additional Help, select Help from the menu bar.^IWLb R       Search Button: This will provide you with a search-list of words appropriate to this application. All topics associated with a given word are displayed.HyperText Links: You can access related information by clicking on any green highlighted word or symbol (). You can also use the Tab key to move among the highlighted words, and then use the Enter key to select the related topic.Printing: You can print information within the help application by selecting File->Print Topic.IrM7 <R Back Button: Displays the topic you viewed prior to the one you are viewing now.History Button: Displays the history of topics you have explored in this session, and allows you to select a particular one for review.9WLM1c%M Keyboard2 rMM' B Keyboard(MO8 >R   The TAB key will move you from field to field. The screen also recomputes each time you leave an editable field. The ENTER key also recomputes the screen each time you press it in an editable field, but the focus does not change.M G \R    Type ALT- to move to a particular placve on the screen, where is the character in the label that is underlined.O rM1O1& Helvs application.Times New Roman).CSymbolun multiple cArialSome error ocTms Rmnrror in initalizing Error in iMS Sans SerifDLLNSCourierHelveticaCourier New ![R*yw 3A m > V) DAuAG(\ !["#$ֈ%&'C()$*H+yGD) A\3 Am>VC$A\HAuAGD) (wGD) \m> ([ֈ/&;)i240: 56BB: ''AboutAndrew Kalotay AssociatesBinomial TreeBond CallsBond Tenders Call Schedule$Callable Bonds(Calls,Certain Cashflows0Certain Option Payouts4Contents8Coupon<Curve@Discount FactorsDDuration menuHDuration, BondsLDuration, Putable BondsPDuration,Callable BondsTEfficiencyXForward Rate Curve`HelpdHelp menuhKeyboardlOptionless BondspPar YIeld CurvetPrincipal FlowsxPrincipals|Put SchedulePutable BondsQualityRefunding menuServicesTendersValuationValuation menuVolatilityYield Curve menuZero Coupon CurveZero Volatility_PUTDURATION d:\c\wpp\primer\primer.rtf 33 >5460C98B HC_CALLS 0 HC_CALLS d:\c\wpp\primer\primer.rtf 34 B97C87C5D HC_TENDERS 0 HC_TENDERS d:\c\wpp\primer\primer.rtf 35 >53F9C1EB HC_ABOUT 0 HC_ABOUT d:\c\wpp\primer\primer.rtf 36 :D63B8985 HC_AKA 1 HC_AKA d:\c\wpp\primer\primer.rtf 36 D5BC22518 HC_SERVICES 1 HC_SERVICES d:\c\wpp\primer\primer.rtf 36 H1DD7D14B HC_PRINCIPALS 1 HC_PRINCIPALS d:\c\wpp\primer\primer.rtf 36 D8314234A HC_PRODUCTS 1 HC_PRODUCTS d:\c\wpp\primer\primer.rtf 36 F60E3C318 HC_QUICKHELP 0 HC_QUICKHELP d:\c\wpp\primer\primer.rtf 37 D47D56F69 HC_KEYBOARD 0 HC_KEYBOARD d:\c\wpp\primer\primer.rtf 38 S7RP6 ;2~uu3_^f]MEUVW^㋟$ ^w  Ƌ׊̊ىN~uvv;WV~ %+;NvN~tQt 6 ;Y^_^GW+}~t ^wFN )Nv눋^w  _^f]M EUVWN^tvSv v 0 ;6J~WvV tG3tA  9D\}SRPVQVS tvڿ _^f]M EUVWv uv޸VvvvPRdWValuing Certain Option PayoutsAndrew Kalotay Associates: ServicesGAndrew Kalotay Associates: PrincipalsAndrew J. KalotayDGeorge O. Williams) C. Douglas Howard: Exclusive ConsultantLicensed ProductsAThe Par Yield CurveThe Forward One-Period Rate CurveֈZero Coupon CurveDiscount FactorsInterest Rate VolatilityZero Volatility WorldVCouponPrincipal Flows3Call SchedulePut ScheduleValuing Optionless Bonds Valuing Callable Bonds(Valuing Putable BondsCDuration for Optionless BondsDuration for Callable Bonds$Duration for Putable BondsACall Efficiency Study\Tender Efficiency StudyyAboutHQuick Help on HelpuKeyboardwwwxwwwwqwwwwxwwww|wqwwwwxwwww|wqwwwxwwwwwwqwwwwxwwwwwwwwwwwxwwwww|wwwwwwwwxwwwww|wwwwwwwwxwwwwwwwwwwwwwwxwwwwwwwwwwwwwwxP: lp vvd:\temp\~hc2MM]M UWV+vv v F+RPFP*F uyv trVxV tcVF&EF&U VWVPF t7^&w&wvP&_&&_F=6uvv uvG~u~t tVGF^_] UWVF+9vuƆxvxP| xd:\temp\~hc2 vxu^ &w v\+gUv v xPFP u2v^&w vF t!Ps tN!D v tv^_] UWVvVxFV t7^&G*~&vvv pP+P+ F FtV uVG^_] Wd:\temp\~hc2FPxFV th~ uƆpv pP|Po"opPFPrF u4vvpPFPF uvv^&w u Fv^&G*^&^&w v R uBPPCv tpWs tdF ^&9GuD&GDN D^KA@=wxwx ̄wwx U\wwx Uwwx Uqw| U\wqw| U/&;)L4Uwwxw|U&&J#FC]|ȗ\F DceeRHӷ;wE%mL$E;ֈnA.ҮAG;3KGrL*eC2>Z69 7H֔@>B(ioGu"PDPVSy=T`TA`rU%[`HybSd) H8Vi) Ymem[Љm|g^F&?t;~g&& tF&7~g+&&^&7G^&>t) t6+6G^&&?}ODF2WV+wF u\WUJ3/]=uJЎ~΋3&E&E!/31r &E u&]"1r &>>E_^_jhhhTFvCFFF +FFFFFFFFa^^&Ga&_v v SFPjh~oFUV^ &G&G +&G&G&G &G &G&G&G&G&v&a&Da&D+&D&D&D &D &D&D&D&D^ &G^&G^UC؋Fd~ tj C،VFFF9d~ ヿdu9du =dtudgd+dd9gtGvjFFV tFdNVdd^㉇dFV^vexe7jBPv+F u+ F^㉇ddvxddC،VFOxedFPvG^LJdd+FHudgd+ddFF9d~(N9du>gtxeveF˸ARWVCظ4^_WVC؃~$F N *^F&F n~u^&*N N *F F ^_ WVCvPh'PPj@tDPj@=@t MZujPj@8: uJj;t.;t%Ph=t NEu(+F~wKPhnF-#FPv;Fu!2Qv5;un n^_PSQR) yZY[X&'u$W'Ht@ ZY[X CDDBEUWQV3PQ(' t^Y_]M3WGGGBOGGG_G`OG _GgGG_G|GOGOG G G GA Gf G GOG.7G G G]_GG_G`OGr_GgGG_G|GOGOG G G lp@@ \wxwx ̄wwx U\wwx Uwwx Uqw| U\wqw| U\wqwUwqwwUwwxw|U\wxw|U\wxwwUwxwwUqwwxww|U\wqqwwxww|U\wqwwxwUwqqwwxwUwqwwxw|U\wx̂wwxwqwwxw|wqwwxw|wqwxwwqwwxwwwwxw|wxw|wxwxwx