$\mathrm{restart}\;$$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{SetEvaluationDate}\left(''November\; 17,\; 2006''\right)\;$

$''December\; 8,\; 2006''$

$\mathrm{payment\_date}:=\mathrm{AdvanceDate}\left(3\,\mathrm{Months}\,\mathrm{NewYork}\,\mathrm{convention}\=\mathrm{Following}\right)\;$

$\mathrm{payment\_date}:=''February\; 20,\; 2007''$

$\mathrm{cash\_flow1}≔\mathrm{SimpleCashFlow}\left(100\,\mathrm{payment\_date}\right)\;$

$\mathrm{cash\_flow1}:=\mathrm{100.\; on\; February\; 20,\; 2007}$

${\mathrm{cash\_flow1}}_{\mathrm{amount}}\;$

$100.$

${\mathrm{cash\_flow1}}_{\mathrm{date}}\;$

$\mathrm{date}$

$\mathrm{eval}\left({\mathrm{cash\_flow1}}_{\mathrm{date}}\right)\;$

$\mathbf{module}\left(\right)\mathbf{option}\mathrm{record}\;\mathbf{export}\mathrm{weekDay}\,\mathrm{monthDay}\,\mathrm{month}\,\mathrm{year}\,\mathrm{format}\;\mathbf{end\; module}$

$\mathrm{FormatDate}\left({\mathrm{cash\_flow1}}_{\mathrm{date}}\right)\;$

$''February\; 20,\; 2007''$

$\mathrm{NetPresentValue}\left(\mathrm{cash\_flow1}\,0.03\right)\;$

$99.22221858$

$\mathrm{NetPresentValue}\left(\mathrm{cash\_flow1}\,0.03\,\mathrm{referencedate}\=''January\; 18,\; 2006''\right)\;$

$96.78169326$

$\mathrm{accrual\_start\_date}:=\mathrm{AdvanceDate}\left(7\,\mathrm{Months}\right)\;$

$\mathrm{accrual\_start\_date}:=''June\; 17,\; 2007''$

$\mathrm{accrual\_end\_date}:=\mathrm{AdvanceDate}\left(\mathrm{accrual\_start\_date}\,3\,\mathrm{Months}\right)\;$

$\mathrm{accrual\_end\_date}:=''September\; 17,\; 2007''$

$\mathrm{cash\_flow2}:=\mathrm{FixedRateCoupon}\left(100\,0.03\,\mathrm{accrual\_start\_date}\,\mathrm{accrual\_end\_date}\right)\;$

$\mathrm{cash\_flow2}:=\mathrm{.7561643836\; on\; September\; 17,\; 2007}$

${\mathrm{cash\_flow2}}_{\mathrm{amount}}\;$

$0.756164383561643838$

$\mathrm{FormatDate}\left({\mathrm{cash\_flow2}}_{\mathrm{date}}\right)\;$

$''September\; 17,\; 2007''$

$\mathrm{NetPresentValue}\left(\mathrm{cash\_flow2}\,0.05\right)\;$

$0.7253214642$

$R:=\mathrm{BenchmarkRate}\left(1\,\mathrm{Months}\,\mathrm{CADLIBOR}\,0.05\right)\;$

$R:=\mathbf{module}\left(\right)\mathbf{end\; module}$

$r:=\mathrm{SquareRootDiffusion}\left(0.045\,0.05\,0.2\,0.03\right)\;$

$r:=\mathrm{\_X}$

$A:=\mathrm{SamplePath}\left(r\left(t\right)\,t\=0..5\,\mathrm{timesteps}\=100\right)\;$

$\mathrm{PathPlot}\left(A\,\mathrm{axes}\=\mathrm{BOXED}\,\mathrm{gridlines}\=\mathrm{true}\,\mathrm{thickness}\=3\right)\;$

$\mathrm{start\_history}:=\mathrm{AdvanceDate}\left(-101\,\mathrm{Days}\right)\;$

$\mathrm{start\_history}:=''August\; 8,\; 2006''$

$\mathrm{LoadHistory}\left(R\,\mathrm{start\_history}\,A\right)\;$

$R\left(''September\; 15,\; 2006''\right)\;$

$0.05804387158$

$R\left(''January\; 10,\; 2007''\right)\;$

$0.04941992695$

$R\left(''November\; 7,\; 2007''\right)\;$

$0.04941992695$

$\mathrm{cash\_flow3}:=\mathrm{InArrearIndexedCoupon}\left(100\,R\,\mathrm{start\_history}\,\mathrm{AdvanceDate}\left(\mathrm{start\_history}\,2\,\mathrm{Years}\right)\right)\;$

$\mathrm{cash\_flow3}:=\mathrm{10.00751462\; on\; August\; 8,\; 2008}$

$\mathrm{NetPresentValue}\left(\mathrm{cash\_flow3}\,0.05\right)\;$

$9.180826599$

$\mathrm{NetPresentValue}\left(\left[\mathrm{cash\_flow1}\,\mathrm{cash\_flow2}\,\mathrm{cash\_flow3}\right]\,0.05\right)\;$

$108.6132094$

$\mathrm{cash\_flows}:=\left[\mathrm{cash\_flow1}\,\mathrm{cash\_flow2}\,\mathrm{cash\_flow3}\right]\;$

$\mathrm{cash\_flows}:=\left[\mathrm{cash\_flow1}\,\mathrm{cash\_flow2}\,\mathrm{cash\_flow3}\right]$

$\mathrm{Convexity}\left(\mathrm{cash\_flows}\,0.05\right)\;$

$0.3175386474$

$\mathrm{Convexity}\left(\mathrm{cash\_flows}\,0.04\right)\;$

$0.3208599232$

$\mathrm{BasisPointSensitivity}\left(\mathrm{cash\_flows}\,0.05\right)\;$

$210.4591831$

$\mathrm{BasisPointSensitivity}\left(\mathrm{cash\_flows}\,0.04\right)\;$

$213.9014542$

$\mathrm{Duration}\left(\mathrm{cash\_flows}\,0.05\right)\;$

$0.3878554142$

$\mathrm{ir}:=\mathrm{InternalRateOfReturn}\left(\mathrm{cash\_flows}\,106\right)\;$

$\mathrm{ir}:=0.1136419342$

$\mathrm{Duration}\left(\mathrm{cash\_flows}\, \mathrm{ir}\right)\;$

$0.3776184776$