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0cm 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1026"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--> </head> <body lang=EN-GB link=blue vlink=purple style='tab-interval:36.0pt'> <div class=WordSection1> <div style='mso-element:para-border-div;border:none;border-bottom:solid #4F81BD 1.0pt; mso-border-bottom-themecolor:accent1;padding:0cm 0cm 4.0pt 0cm'> <p class=MsoTitle align=center style='text-align:center'><span lang=EN-US>Homework exercises</span></p> </div> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Test <span class=SpellE>PRand</span> using the <a href="http://www.iro.umontreal.ca/~simardr/testu01/tu01.html">TestU01</a> test suite (e.g. Little Crush or Big Crush).<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Create and test a variant of <span class=SpellE>PRand</span> <span class=SpellE>eg</span>. <span class=GramE>D2(</span>A2<sub>l</sub>), and compare with the test results from <span class=SpellE>PRand</span>.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family: Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin; mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'>Apply the Chi-squared test (as described in <span class=MathematicaFormatTextForm>Thomas, <span class=SpellE>Luk</span>, Leong and <span class=SpellE>Villasenor</span> 2007 : 11  25) to a random samples generated by <o:p></o:p></span></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></span><![endif]><span class=SpellE><span class=MathematicaFormatTextForm><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NRand</span></b></span></span><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'>()<span style='mso-spacerun:yes'> </span>(<span class=SpellE>PRand</span> + Moro)<o:p></o:p></span></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></span><![endif]><span class=SpellE><span class=MathematicaFormatTextForm><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NormSInv</span></b></span></span><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'>(<b style='mso-bidi-font-weight:normal'>Rand</b>())<o:p></o:p></span></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt'><span class=GramE><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>and</span></span></span><span class=MathematicaFormatTextForm><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'> compare the results. <i style='mso-bidi-font-style:normal'>This exercise can be done in Excel</i>.</span></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>4)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Compute a bounding rectangle <i style='mso-bidi-font-style:normal'>B</i> for the acceptance region <i style='mso-bidi-font-style:normal'>A</i> for the ratio-of-uniforms method applied to the normal distribution.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>5)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Calibri;mso-bidi-theme-font:minor-latin'>Generate 100 standard normal random variables using the <b style='mso-bidi-font-weight:normal'>ratio-of-uniforms</b> method, and test for normality, using </span><span lang=EN-US style='font-size: 11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>The Jacques-<span class=SpellE>Bera</span> test</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>The Kolmogorov-Smirnov Test.</span><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>6)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Calibri;mso-bidi-theme-font:minor-latin'>Generate 100 standard normal random variables using the <b style='mso-bidi-font-weight:normal'>Moro</b> or <span class=SpellE><b style='mso-bidi-font-weight:normal'>Wichura</b></span> transforms, and test for normality, using </span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>The Jacques-<span class=SpellE>Bera</span> test</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>The Kolmogorov-Smirnov Test.</span><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Compare the test results and the computation time with the ratio-of-uniforms method.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>7)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Calibri;mso-bidi-theme-font:minor-latin;background:lime;mso-highlight:lime'>Write a program to generate a list of random option parameters Type, S, K, r, , T as follows</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Calibri;mso-bidi-theme-font:minor-latin'>:</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'>Call with probability 0.5, put with probability 0.5.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>S = 100</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>K ~ U[70,130]</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>r ~ U[0,0.10] with probability 0.8, r = 0 with probability 0.2</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'> ~ U[0.1,0.6]</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 36.0pt;text-indent:-18.0pt;mso-list:l0 level2 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:Symbol;mso-fareast-font-family: Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>T ~ U[0.1,1] with probability 0.75, T ~ U[1,5] with probability 0.75</span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Each line should contain the parameters for one option, separated by commas (CSV format).<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>8)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Write a program to value vanilla European options (calls and puts), using the <span class=SpellE><b style='mso-bidi-font-weight:normal'>PRand</b></span> random number generator and the Moro transformation. The program should read option parameters from a file, and print a value for each option.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>9)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Extend the previous program to optionally output a convergence table. We will call this <span class=SpellE><b style='mso-bidi-font-weight:normal'>VanillaOption</b></span>.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>10)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>If you want a programming challenge, implement a GUI interface for <span class=SpellE>VanillaOption</span>. Call it <span class=SpellE><b style='mso-bidi-font-weight:normal'>VanillaOptionG</b></span>.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>11)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Using <span class=SpellE>VanillaOption</span>, value a European call option </span><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt; font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin;mso-bidi-font-family:Times'>S</span></i><sub><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Times'>0</span></sub><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Times'> = 100, <i style='mso-bidi-font-style:normal'>r</i> = 5<span class=GramE>% ,</span> <i style='mso-bidi-font-style:normal'>q</i> = 1%,  = 20%, and <i style='mso-bidi-font-style:normal'>T</i> = 1, with a confidence interval of </span><span lang=EN-US style='font-family:"Times","serif"'>1 cents (i.e. 0.01).</span><span lang=EN-US style='font-size:11.0pt;font-family: "Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'><o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>12)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Amend VanillaOption1 to implement antithetic variables. Call this the <span class=SpellE><b style='mso-bidi-font-weight:normal'>VanillaOptionAV</b></span>.<o:p></o:p></span></p> <p style='margin-top:7.5pt;margin-right:0cm;margin-bottom:5.0pt;margin-left: 18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>13)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Apply <span class=SpellE>VanillaOptionAV</span> to value the European call option with a </span><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif"; mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: Times'>confidence interval of </span><span lang=EN-US style='font-family:"Times","serif"'>1 cents (i.e. 0.01).</span><span lang=EN-US style='font-size:11.0pt;font-family: "Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'><o:p></o:p></span></p> </div> </body> </html>