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Ch Refinance ng Equity s Www U Agricultural i Tag g Agricultural usearcha Agricultural ionsearchYea Agricultural Bank tsearchA Equity t Equity C, China Equity PA*(1+YTM)t Ct,B t*Ct,B /PB*(1+YTM)t Actual Bond DP D P Dr -DPDr/(1+r) A B Bond price Duration Excel formula graph title Effect of Maturity on Duration coupon Reminder: Duration(settlement, maturity, coupon, yield, frequency, basis) Effect of Coupon on Duration Alpha N Number of payments Coupon Face Period Payment Checking on formula: the bond duration (with first payment at alpha) should be the duration of the bond with payments at 1, 2, ..., 5 plus (alpha-1): testing whether Excel¡®s duration function produces the same result: settlement month maturity day alpha ytm Current date Annual coupon Paid January 1 for each of next 5 years Maturity date Face value Price of bond Time to first payment Date ILLUSTRATION OF CALCULATION OF YTM OF UNEVEN PERIODS This spreadsheet illustrates the unevenYTM VBA function: Coupon rate Time to first payments Epsilon =NPV(B3,B6:B15) =SUM(F6:F15) Using Excel¡®s MDurati¡¡¡¡
190 Page 246 Page 187 Page 181 chart Page 181 Page 180 Page 186 chart Page 185 chart Page 184 chart Page 183, chart Page 183 chart Page 177-179 £¨ÖÐÎÄ£© Page 177-179 Page 178-179 (ÖÐÎÄ) Page 178-179 getformula Profit Patterns from GP Stock and Options Initial GP stock price Terminal GP stock price stock Bought Written price call put Call price, July Bought call profit Written call profit Put price, July Bought put profit Written put profit Terminal Call exercise price Put exercise price <-- Data table header Profit Patterns from a Spread <-- Data table header, hidden Option time to maturity, T Option exercise price, X Interest rate, r Current stock price, S0 Call Option Payoff Patterns Purchase call option, cash flow < 0 Between times 0 and T: Cash flow = 0 for European option Cash flow > 0 for American option Write (I.e., issue) call option, cash flow > 0 Between times 0 and T: Cash flow = 0 for European option Cash flow < 0 for American option Cash flows of call buyer Put Option Payoff Patterns Purchase put option, cash flow < 0 Cash flows of put buyer Cash flows of put writer Cash flows of call writer Naive minimum put option price, Max(X- S0,0) Time 0 Time 1 <-- =MAX(B3-B5,0) <-- =MA¡¡¡¡
Page 86a (ÖÐÎÄ) Page 86a Page 86 (ÖÐÎÄ) Page 86 Page 84 (ÖÐÎÄ) Page 84 Page 82-83 (ÖÐÎÄ) Page 82-83 Page 80 (ÖÐÎÄ) Page 80 solver_adj solver_adj solver_adj solver_adj solver_cvg 1.00E-04 solver_cvg 1.00E-04 solver_drv 1.00 solver_drv 1.00 solver_est 1.00 solver_est 1.00 solver_itr 100.00 solver_itr 100.00 solver_lin .00 solver_lin .00 solver_lin 2.00 solver_lin 2.00 solver_neg 2.00 solver_neg 2.00 solver_num .00 solver_num .00 solver_num .00 solver_num .00 solver_nwt 1.00 solver_nwt 1.00 solver_opt solver_opt solver_opt solver_opt solver_pre 1.00E-06 solver_pre 1.00E-06 solver_scl 2.00 solver_scl 2.00 solver_sho 2.00 solver_sho 2.00 solver_tim 100.00 solver_tim 100.00 solver_tol .05 solver_tol .05 solver_typ 3.00 solver_typ 3.00 solver_typ 3.00 solver_typ 3.00 solver_val .08 solver_val .08 solver_val .07 solver_val .07 Misleading analysis: This is the analysis of the first section of the chapter Asset cost these numbers are copied Interest rate from the next spreadsheet Lease rental payment Annual depreciation Tax rate NPV(leasing) NPV(buying) Principal Loan Of which After-tax at beginning payment, Repayment loan Year of year end of year Interest of principal repayment After-tax cash flows f¡¡¡¡
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Page 171, (ÖÐÎÄ) Page 171, Page 169-172 Page 174 card card output1 output1 output2 output2 output3 output3 output4 output4 output5 output5 printarea printarea random1 random1 random2 random2 random3 random3 random4 random4 random5 random5 number random output1 H E L N Helen¡®s 85th Birthday bingo game!!! This column is called "random1" Note: Ctrl + A works macro. Output1 Random Output2 Output3 Output4 Output5 Note: The macro which prints new Bingo cards works only on the Page 224 file. ¼¼ÇɵÄ˵Ã÷ Êý×Ö Ëæ»úÊý HelenµÄ µÚ85¸öÉúÈÕ ±ö¹ûÓÎÏ·!!! ½á¹û1 ½á¹û2 ½á¹û3 ½á¹û4 ½á¹û5 ×¢Òâ:Ctrl + A ÔËÐкꡣ 11.00 34.00 40.00 54.00 74.00 14.00 28.00 36.00 61.00 82.00 12.00 18.00 45.00 65.00 73.00 10.00 23.00 37.00 63.00 84.00 8.00 20.00 39.00 59.00 78.00 11.00 .06 34.00 .02 40.00 2.41E-04 54.00 .09 74.00 .03 14.00 .06 28.00 .11 36.00 .07 61.00 .10 82.00 .04 12.00 .24 18.00 .16 45.00 .08 65.00 .10 73.00 .09 10.00 .27 23.00 .16 37.00 .11 63.00 .17 84.00 .21 8.00 .35 20.00 .26 39.00 .13 59.00 .21 78.00 .24 16.00 .37 27.00 .39 50.00 .15 67.00 .27 80.00 .25 15.00 .¡¡¡¡
VBA routines Pictures Early exercise (ÖÐÎÄ) Early exercise Page 270(ÖÐÎÄ£© Page 270 divrate divrate divrate interest interest interest mean mean mean n n n n output output output S S S S Sigma Sigma Sigma Sigma T T T T X X X X T t=0 t=0.25 t=0.5 t=0.75 t=1 X S n Suu Su S Sud Sd Sdd Cuu = max[X-Suu,qu*max(X-Suuu,0)+qd*max(X-Suud,0)] X-Su > qu*Cuu + qd*Cud max(X-Suuu,0) max(X-Suud,0 max(X-Sudd,0) max(X-Sddd,0) Cud = Cdu = max[X-Sud,qu*max(X-Sudu,0)+qd*max(X-Sudd,0)] Cdd = max[X-Sdd,qu*max(X-Sudd,0)+qd*max(X-Sddd,0)] Cud = Cdu = X-Sud Cdd = X-Sdd <-- =((1-E14)*B9-B5)/(B4-B5) <-- =(B4-(1-E14)*B9)/(B4-B5) Mean Sigma r <-- =E13/4 Early Îå¸öʱÆÚµÄÃÀ¹ú¶þÏî¿´ÕÇÆÚȨ¶¨¼Û ״̬¼Û¸ñ ¹ÉÀûÂÊ exp[6%/4] -1 ÉÏÕÇ-ϵø--°üº¬¹ÉÀû ÉÏÕÇ qu ϵø qd ³õʼ¹ÉƱ¼Û¸ñ Ö´Ðм۸ñ 1+r(Dt) ×¢Òâ:ʱÆÚ T = 1 ±»·Ö³É4¸ö×ÓʱÆÚ¡£ ÿÆÚµÄ"ÉÏÕÇ"¶¨ÒåΪ exp[mean*Dt+sigma*sqrt(Dt)]£¬"ϵø" Ϊexp[mean*Dt-sigma*sqrt(Dt)] , ÕâÀï mean = 20% and sigma = 60%¡£ 6%µÄÄêÀûÂÊÿ¸ö×ÓʱÆÚµÄÀûÂÊΪ£º 8%µÄ¹ÉÀûÂÊ·ÖËÄ´ÎÖ§¸¶¡£ Äê ÔÚ Dt °üº¬¹ÉÀûµÄ¹ÉƱ¼Û¸ñ ¹ÉÀûÂÊ ÀûÂÊ ¹ÉƱƽ¾ùÊÕÒæ ¹ÉƱÊÕÒæµÄ±ê×¼²î °´[Ctrl]+a¼ü£¬Ö´ÐкêÃüÁî ʱ¼ä ½çÏÞ <-- Ϊ Dt = T/n °´[Ctrl]+a¼ü£¬Ö´ÐкêÃüÁî <-- Ϊ Dt = T/n ʱ¼ä ÌáÔçÖ´ÐÐ ½çÏÞ ¹ÉƱ¼Û¸ñ ³ýÏ¢ºóµÄ¹ÉƱ¼Û¸ñ ¹ÉÀû£º ÉÏÃæÁ½¸öÊ÷µÄ²î¶î ÃÀ¹úʽ¿´ÕÇÆÚȨ¼Û¸ñ ÔÚ³ýÏ¢ºó¹ÉƱÉϵÄÅ·ÖÞʽ¿´ÕÇÆÚȨ¼Û¸ñ ÌáǰִÐÐ¸ÃÆÚȨ ĿǰµÄ¹É¼Û ÆÚȨִÐм۸ñ ÀûÂÊ ¶ÔÊýÕý̬´¦ÀíµÄ¾ùÖµm ¶ÔÊýÕý̬´¦ÀíµÄ±ê×¼²î s ÌáǰִÐÐ Ò»¸öÃÀ¹úʽ¿´ÕÇÆÚȨÌáǰִÐнçÏÞ ÃÀ¹úʽ¿´µøÆÚȨ δµ½ÆÚ£¨Î´Ö´ÐУ©µÄÉÏÕÇÆÚȨµÄ¼ÛÖµ ÅÉϢǰ¹ÉƱÉϵÄÅ·ÖÞÆÚȨµÄ¼ÛÖµ FIVE DATE AMERICAN BINOMIAL CALL OPTION PR¡¡¡¡
Page 167-168 (ÖÐÎÄ) Page 167-168 Page 166 bottom (ÖÐÎÄ) Page 166 bottom Page 166 Page 165 (ÖÐÎÄ) Page 165 Page 163 (ÖÐÎÄ) Page 163 Page 162-163, (ÖÐÎÄ) Page 162-163, Page 161 (ÖÐÎÄ) Page 161, elapsed exchangerand iiterations iiterations indexrand interestrand iterations meanreturn Returndata solver_adj solver_adj solver_adj solver_adj solver_cvg 1.00E-04 solver_cvg 1.00E-04 solver_cvg 1.00E-03 solver_cvg 1.00E-03 solver_drv 1.00 solver_drv 1.00 solver_drv 1.00 solver_drv 1.00 solver_est 1.00 solver_est 1.00 solver_est 1.00 solver_est 1.00 solver_itr 100.00 solver_itr 100.00 solver_itr 100.00 solver_itr 100.00 solver_lin 2.00 solver_lin 2.00 solver_lin 2.00 solver_lin 2.00 solver_neg 2.00 solver_neg 2.00 solver_neg 2.00 solver_neg 2.00 solver_num .00 solver_num .00 solver_num .00 solver_num .00 solver_nwt 1.00 solver_nwt 1.00 solver_nwt 1.00 solver_nwt 1.00 solver_opt solver_opt solver_opt solver_opt solver_pre 1.00E-06 solver_pre 1.00E-06 solver_pre 1.00E-06 solver_pre 1.00E-06 solver_scl 2.00 solver_scl 2.00 solver_scl 2.00 solver_scl 2.00 solver_sho 2.00 solver_sho 2.00 solver_sho 2.00 solver_sho 2.00 solver_tim 100.00 solver_tim 100.00 solver_tim 100.00 solver_tim 100.00 solver_tol .05 solv¡¡¡¡
Page 458 Arrays ArrayAssign ArrayDemo1 ArrayDemo3 ArrayDemo4 ArrayDemoBase1 DynPV Matrix1 Matrix2 MoreDynPV NewDynPV VarArrayAssign VarPV VarPV In Action CF VarPV <-- =VarPV(A4:A$8) <-- =VarPV(A5:A$8) <-- =VarPV(A6:A$8) <-- =VarPV(A7:A$8) <-- =VarPV(A8:A$8) <-- =NPV(0.05,A4:A$8) <-- =NPV(0.05,A5:A$8) <-- =NPV(0.05,A6:A$8) <-- =NPV(0.05,A7:A$8) <-- =NPV(0.05,A8:A$8) NPV Macros in this Workbook ArrayDemo1() ArrayDemo3() ArrayDemo4() ArrayDemoBase1() Matrix1() Matrix2() MoreDynPV() DynPV() ArrayAssign() VarArrayAssign() NewDynPV() 100.00 432.95 432.95 .05 100.00 354.60 354.60 .05 100.00 272.32 272.32 .05 100.00 185.94 185.94 .05 100.00 95.24 95.24 .05 Function"s first reference is on page 467 This verssion first reference is on page 466 Function VarPV(CF As Variant) As Double Dim X As Variant Dim Temp As Double Dim i As Integer X = CF Temp = 0 If IsArray(X) Then For i = LBound(X) To UBound(X) Temp = Temp + X(i, 1) / 1.05 ^ i Next i Else Temp = X / 1.05 End If VarPV = Temp End Function Placing the cursor on a cell with a small red triangle in the corner will show you the source code of the Function To edit the code you may press [Alt-F11] and look for a module called Chapter. The Funct¡¡¡¡
Page 225 (ÖÐÎÄ) Page 225 Page 224 chart (ÖÐÎÄ) Data for page 224 chart Page 224 chart Page223 Page222 (ÖÐÎÄ) VBA program, pages 189-190 benny benny benny Counter Counter Counter elapsed elapsed elapsed initial_price initial_price initial_price mean mean mean output output output runs runs runs sbenny sbenny sbenny sigma sigma sigma starttime starttime starttime stoptime stoptime stoptime Stock Starttime Runs chart title Day price Stoptime Initial price Lognormal Price Simulation Elapsed Mean Sigma for some runs of the simulation. Monthly Month Price return Monthly average Monthly standard deviation =STDEVP(C6:C17) Annual average Annual standard deviation Calculating Lognormal Mean and Sigma from Stock Price Data Simulating Lognormal Price Paths with VBA press Ctrl+A to operate macro Note that here Application.screenupdating makes a big difference! Note: You may have to rescale the y-axis on the graph <-- =AVERAGE(C6:C17) <-- =LN(B6/B5) <-- =LN(B7/B6) <-- =C19*12 <-- =C20*SQRT(12) °´Ctrl+AÔËÐкêÃüÁî ×¢ÒâÕâÀïApplication.screenupdatingÓÐÒ»¸öºÜ´óµÄ²îÒì! Ìì ¹ÉÆ± ¿ªÊ¼Ê±¼ä ֹͣʱ¼ä ÊÅȥʱ¼ä ÔËÐÐ ³õʼ¼Û¸ñ ¾ùÖµ ±ê×¼²î ×¢Òâ:Äã¿ÉÒÔµ÷ÕûÔËÐиÃÄ£ÄâµÄͼÐεÄYÖá¿Ì¶È ¸ù¾Ý¹ÉƱ¼Û¸ñÊý¾Ý¼ÆËã¶ÔÊýÕý̬·Ö²¼µÄ¾ùÖµºÍ±ê×¼²î Ô ¼Û¸ñ ÔÂÊÕÒæ ÔÂÆ½¾ù Ô±ê×¼²î ÄêÆ½¾ù Äê±ê×¼²î ÓÃVBAÄ£Äâ¶ÔÊýÕý̬·Ö²¼¼Û¸ñµÄ×ßÊÆ Page .00 12.00 1.00 12.90 .07 2.¡¡¡¡
Page 316£¨ÖÐÎÄ£© Page 316 Page 315 (ÖÐÎÄ) Page 315 Page 314 (ÖÐÎÄ) Page 314 Page 311£¨ÖÐÎÄ£© Page 311 Page 310£¨ÖÐÎÄ£© Page 310, Page 309, (ÖÐÎÄ) Page 309, Page 307 (ÖÐÎÄ) Page 307 bondterm bondterm initial initial matrixpower payoff1 payoff1 payoff2 payoff2 solver_adj solver_adj solver_lin .00 solver_lin .00 solver_num .00 solver_num .00 solver_opt solver_opt solver_typ 3.00 solver_typ 3.00 solver_val .09 solver_val .09 transition transition EXPECTED RETURN ON A ONE-YEAR BOND WITH AN ADJUSTMENT FOR DEFAULT PROBABILITY Face value, F Price, P Annual coupon rate, Q Recovery percentage, l Expected cash flow <-- =B7*(1+B6)*B4+(1-B7)*B8*B4 Expected return <-- =B10/B5-1 One-period transition matrix Two-period transition matrix Three-period transition matrix USING THE FUNCTION MATRIXPOWER t CALCULATING THE EXPECTED BOND RETURN Bond price Payoff(tVBA routines Early exercise£¨ÖÐÎÄ) Early exercise Page 265£¨ÖÐÎÄ£© Page 265 Page 264(ÖÐÎÄ£© Page 264 getformula interest interest interest n n n output output output S S S Sigma Sigma Sigma T T T X X X qu qd Bond price 1+r(Dt) T t=0 t=0.25 t=0.5 t=0.75 t=1 S X Sigma n r B-S <-- (LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) Interest, r Graph title: values of n change. The formula in cell J5 is: ="American Put Early Exercise Boundary, n = "&TEXT(n,"0") To learn more about how to do this, see Chapter 30. d1 d2 <-- d1 - sigma*SQRT(T) N(d1) N(d2) <-- S*N(d1)-X*exp(-r*T)*N(d2) ²¼À³¿Ë-˹¿Æ¶û˹(B-S)ÆÚȨ¶¨¼ÛÄ£ÐÍ µ±Ç°¹ÉƱ¼Û¸ñ Ö´Ðм۸ñ ÎÞ·çÏÕÀûÂÊ ÆÚȨµÄµ½ÆÚʱ¼ä£¨Ä꣩ ¹ÉƱµÄ²¨¶¯ÐÔ <-- ʹÓõĹ«Ê½NormSDist(d1) <-- ʹÓõĹ«Ê½NormSDist(d2) ¿´ÕÇÆÚȨ¼Û¸ñ ¿´µøÆÚȨ¼Û¸ñ <-- ¿´ÕÇÆÚȨµÄ¼Û¸ñ - S + X*Exp(-r*T):¸ù¾Ý¿´ÕÇ-¿´µøÆÚȨƽ¼Û ¹ÉƱ ÄÚÔÚ ¼Û¸ñ ¼ÛÖµ µ±¹ÉƱ¼Û¸ñµÍʱ£¬¿´µøÆÚȨµÄ²¼À³¿Ë-˹¿Æ¶û˹£¨B-S£©¼ÛֵСÓÚÄÚÔÚ ¼ÛÖµ¡£Èç¹ûÎÒÃÇÌáǰִÐУ¬¸ÃÆÚȨµÄ¼ÛÖµ¿ÉÄÜ»áÔö¼Ó¡£Òò´Ë£º ¶Ô¸Ã¿´µøÆÚȨÌáǰִÐпÉÄÜÊÇÓмÛÖµµÄ¡£ ÎåʱÆÚµÄÃÀ¹ú¶þÏî¿´µøÆÚȨµÄ¶¨¼Û ÉÏÕÇ ×´Ì¬¼Û¸ñ ϵø ³õʼµÄ¹ÉƱ¼Û¸ñ ×¢Òâ: ÆÚ¼äT = 1±»·Ö³É4¸ö×ÓÆÚ¼ä ÿ¸öÆÚ¼äµÄ"ÉÏÕÇ"¶¨ÒåΪexp[s*Dt]-1 "ϵø"¶¨ÒåΪexp[-s*Dt]-1,ÕâÀï s = 40%,ÿ¸ö×ÓÆÚ¼ä½«8%µÄÄêÀûÂÊ ·ÖɢΪexp[8%/4] -1 ¹ÉƱ¼Û¸ñ£º»È¦µÄµ¥Ôª¸ñ±íʾִÐÐ¸ÃÆÚȨ ÃÀ¹úʽ¿´µøÆÚȨµÄ¼Û¸ñ Å·ÖÞʽ¿´µøÆÚȨµÄ¼Û¸ñ Ò»¸öÃÀ¹ú¿´µøÆÚȨµÄÌáǰִÐнçÏÞ °´[Ctrl]+aÔËÐкêÃüÁî ¿´µøÆÚȨִÐм۸ñ ÀûÂÊ Note: This graph title is dynamic--it changes with Ö´ÐÐʱ¼ä <-- Òâ˼ÊÇDt = T/n ʱ¼ä ÌáǰִÐÐ ½çÏÞ FIVE DATE AMERICAN BINOMIAL PUT OPTION PRICING Note: The period T = 1 is divid¡¡¡¡
Page 437 Page 427-436 ConcatDemo MsgBoxDeafault MsgBoxDemo MsgBoxOKCancel PVCalculator SayHi MsgBoxDeafault() MsgBoxOKCancel() MsgBoxDemo() PVCalculator() SayHi() Macros in this Workbook ConcatDemo in Action Parameter1 Parameter2 <-- =ConcatDemo(A4,B4) Ben Jerry <-- =ConcatDemo(A5,B5) <-- =ConcatDemo(A6,B6) <-- =ConcatDemo(A7,B7) 1.00 2.00 12 BenJerry 1.00 Ben1 2.00 Jerry2 Function¡®s first reference is on page 437 Function ConcatDemo(Parameter1, Parameter2) ConcatDemo = Parameter1 & Parameter2 End Function Placing the cursor on a cell with a small red triangle in the corner will show you the source code of the Macro or Function To edit the code you may press [Alt-F11
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