Python for Finance

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Chapter 3Appendix C – Derivation of present value ofannuity from present value of one future cashflow and present value of perpetuityFirst, we have the following two formulae:Here, FV is the future value, R is the discount period rate, n is the number of periods,and C is the same cash flow happening at the end of each period with the first cashflow happening at the end of the first period.[ 99 ]
Time Value of MoneyAn annuity is defined as a set of equivalent cash flows occurring in the future. If the firstcash flow occurs at the end of the first period, the present value of an annuity is bythe following formula:Here, C is a recursive cash flow happening at the end of each period, R is perioddiscount rate, and n is the number of periods. Equation (3) is quite complex. However,with a little bit of imagination, we could combine equations (1) and (2) to deriveEquation (3). This can be done by decomposing an annuity into two perpetuities:This is equivalent to the following two perpetuities:Conceptually, we could think this way: Mary would receive $20 per year for thenext 10 years. This is equivalent to two perpetuities: she would receive $20 everyyear forever and at the same time PAY $20 every year forever, starting at year 11.Thus, the present value of her annuity will be the present value of the first perpetuityminus the present value of her second perpetuity:If the same cash flow happens at the same interval forever, it is called perpetuity. Ifthe discount rate is a constant and the first cash flows happens at the end of the firstperiod, its present value has the following.[ 100 ]
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Python for FinanceSecond EditionFin
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CreditsAuthorYuxing YanProject Coor
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I would like to thank Ben Amoako-Ad
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www.PacktPub.comeBooks, discount of
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Table of ContentsPrefaceixChapter 1
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Table of ContentsAppendix F -how to
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Table of ContentsAppendix C - data
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Table of ContentsCapital budgeting
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PrefaceIt is our firm belief that a
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PrefaceChapter 2, Introduction to P
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PrefaceChapter 13, Credit Risk Anal
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ConventionsIn this book, you will f
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PrefaceErrataAlthough we have taken
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Python BasicsThere are several reas
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Python BasicsThe top-left panel (wi
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Python Basics4. From the IPython sh
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Python BasicsIn the preceding codes
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Python Basics(1+r)^nfv: fture value
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Python BasicsAssuming that we inves
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Python BasicsBy using a loop, we ca
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Python BasicsThe print() function c
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Python BasicsWe could retrieve data
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Python BasicsData typesDescriptioni
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Python BasicsFor example, from the
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Python BasicsIn Chapter 3, Time Val
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Python BasicsTo retrieve the file,
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Python BasicsHere PV is the present
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Introduction toPython ModulesIn thi
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Chapter 2In addition, when a module
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Chapter 2Recall that in Chapter 1,
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Chapter 2To find a specific module,
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Chapter 2In the previous example, d
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Chapter 2----------a : array_likeCa
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Chapter 2If n returns are given, th
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Chapter 2Similarly, we could save a
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Chapter 2The next example presents
Page 76 and 77: Chapter 2Introduction to statsmodel
Page 78 and 79: Chapter 2From the preceding output,
Page 80 and 81: Chapter 2'core', 'crosstab', 'cut',
Page 82 and 83: x[bad] = np.nan# missing code is np
Page 84 and 85: [ 57 ]Chapter 2For finance, time se
Page 86 and 87: Chapter 2Stock A Stock B0 0.452820
Page 88 and 89: Chapter 22010-01-08 110.929466>> >d
Page 90 and 91: Chapter 2After clicking the logo sh
Page 92 and 93: For a Mac, we have the following co
Page 94 and 95: Chapter 2After answering y, the fol
Page 96: Chapter 213. What is wrong with the
Page 99 and 100: Time Value of MoneyIntroduction to
Page 101 and 102: Time Value of MoneyLater in this ch
Page 103 and 104: Time Value of MoneyNote that in the
Page 105 and 106: Time Value of MoneyFor perpetuity,
Page 107 and 108: Time Value of MoneyExample 1: >>>pv
Page 109 and 110: Time Value of MoneyThe following ta
Page 111 and 112: Time Value of MoneyExample 1: >>>pv
Page 113 and 114: Time Value of MoneyIf using the sam
Page 115 and 116: Time Value of MoneyWhile using just
Page 117 and 118: Time Value of MoneyThe related grap
Page 119 and 120: Time Value of MoneyNow, let's write
Page 121 and 122: Time Value of MoneyFor annuity due,
Page 123 and 124: Time Value of MoneyThe total future
Page 125: Time Value of MoneyNormally, if a s
Page 129 and 130: Time Value of MoneyTo find out the
Page 131 and 132: Time Value of MoneyThe output is sh
Page 133 and 134: Time Value of Moneydef pvGrowingAnn
Page 135 and 136: Time Value of Money15. We know that
Page 137 and 138: Sources of DataDiving into deeper c
Page 139 and 140: Sources of DataTo find the usage of
Page 141 and 142: Sources of DataTo view the first an
Page 143 and 144: Sources of DataIn the preceding pro
Page 145 and 146: Sources of Data>>>ret[0:3]array([-0
Page 147 and 148: Sources of DataAssume that two pric
Page 149 and 150: Sources of Datad0=x.datefor i in ra
Page 151 and 152: Sources of DataThe so-called candle
Page 153 and 154: Sources of DataRetrieving data from
Page 155 and 156: Sources of DataAssume that the data
Page 157 and 158: Sources of DataGenerating two dozen
Page 159 and 160: Sources of Data15 spreadBBB Moody's
Page 161 and 162: Sources of Data0 201512311 20130228
Page 163 and 164: Sources of DataAssume that TORQcq.p
Page 165 and 166: Sources of Datasigma = np.std(ret)x
Page 167 and 168: Sources of DataAppendix C - Python
Page 169 and 170: Sources of DataThe corresponding gr
Page 171 and 172: Sources of DataAppendix F -how to g
Page 173 and 174: Sources of Data3. Manually download
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Bond and Stock ValuationBond or fix
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Chapter 5In Chapter 3, Time Value o
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Chapter 5On the bottom, we have the
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Chapter 5By applying equation (8),
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Chapter 5Note that Rm=APR/m is from
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Chapter 5Interest rate quotationEff
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Chapter 5The related graph is given
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Chapter 5For this reason, a Python
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Chapter 5>>>w20.4878049>>>w1*1 + w2
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Chapter 5If a bond holder could con
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Based on this result, the YTM is 7.
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Chapter 5Stock valuationThere are s
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Chapter 5……(23)The selling pric
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Chapter 5Here,Equity is the market
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Here, PV is the present value, R is
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Chapter 5Appendix C - Python progra
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Chapter 5sellingPrice/(1+R)**nselli
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Chapter 5A3/A- 32.00 49.00 59.00 72
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Capital Asset Pricing ModelCapital
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Chapter 6Here is the covariance bet
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Chapter 6Here, yi is the ith observ
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default to the md5 hash or the url
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Chapter 6(beta,alpha,r_value,p_valu
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Chapter 60 1.0 NaN 1.51 1.5 1.0 2.0
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Chapter 6The first 10 lines are sho
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Chapter 6Saving our data to an Exce
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Simple string manipulationFor Pytho
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Chapter 6The output is shown here:T
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Chapter 6The two most used panels a
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Chapter 6ReferencesPlease refer to
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Chapter 6Note 2 - how to download a
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Chapter 616. From this chapter, we
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Multifactor Models andPerformance M
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The pandas DataFrame is used to con
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Chapter 7import statsmodels.api as
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Chapter 7When ratios of equity book
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Chapter 7To save space, we will not
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Chapter 7The corresponding output i
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Chapter 7The output is shown here:P
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Chapter 7The only modification is t
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Chapter 7y = pd.DataFrame({'key': [
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Chapter 7'SP500': [0.1,0.17, -0.05,
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Chapter 7Sometimes, we need to merg
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Appendix A - list of related Python
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Chapter 7The first and last several
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Chapter 7• http://canisius.edu/~y
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14. Data source: http://mba.tuck.da
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Time-Series AnalysisIn finance and
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There is one end of chapter problem
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Chapter 8In the preceding program,
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Function Description Examplesrelati
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Chapter 8The output is shown here:P
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ticker='IBM'begdate=(2013,1,1)endda
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Chapter 8Here, v2(v1) is the second
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2016-09-01 0.0025 0.0200 -0.0134 0.
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Chapter 8import numpy as npticker='
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Chapter 8Some books distinguish the
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Chapter 8ticker='ibm'begdate=(2013,
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Chapter 852-week high and low tradi
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Chapter 8The covariance between the
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ff=pd.read_pickle('c:/temp/ffDaily.
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Chapter 8The following Python progr
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Chapter 8Here, n is the number of o
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Chapter 8x=np.array(pd.read_csv(pat
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Chapter 8The output is shown here:[
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Chapter 8In the preceding example,
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Chapter 8• George, T.J., and Hwan
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The key part of the program used to
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Chapter 8For readers from schools w
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11. In addition, generate the simil
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Portfolio TheoryUnderstanding portf
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Chapter 9Here, is the portfolio var
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Chapter 9var=w1**2*var1 +w2**2*var2
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Chapter 9The graph is shown here:To
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Chapter 9Optimization terminated su
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Chapter 9Here, U is the utility fun
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Chapter 9print("meanAnnual, varAnnj
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[ 303 ]Chapter 9'SCD' 'SEF' 'SI' 'S
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output.columns=[ticker]return outpu
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The key command used is ret.T*ret.
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Chapter 9def sharpe(R,w):var = port
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2. Code for defining two functions:
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Chapter 9In one of the previous pro
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Chapter 9The output is shown here:A
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Chapter 9ret = sp.array(mean_return
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Chapter 9x = getData(ticker,begdate
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Chapter 9Here is the output:Since t
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Chapter 97. Click CSV on the right-
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Chapter 90 10006 19570301 198407181
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Chapter 911. For several stocks suc
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Chapter 910. Update yanMonthly.pkl,
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Chapter 916. Estimating the Sharpe
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Options and Futures• Using the bi
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Options and FuturesTaking the natur
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Options and Futuress0=1.25rHome=0.0
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Options and FuturescontractFuturesS
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Options and FuturesTo create a grap
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Options and FuturesA graphical repr
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Options and FuturesEuropean versus
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Options and FuturesGenerating our o
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Options and FuturesThe first line o
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Options and FuturesThe related grap
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Options and Futuresx3=60; c3=5y1=(a
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Options and FuturesThe correspondin
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Options and FuturesNote that in the
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Options and FuturesOn the other han
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Options and FuturesThe following co
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Options and FuturesThe correspondin
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Options and Futuresplt.figtext(0.75
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Options and FuturesHere, u is the u
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Options and Futures# at level 2su=r
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Options and Futuresd = 1.0 / ua = e
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Options and FuturesFor the currency
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Options and FuturesSimilarly, we co
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Options and FuturesvolHigh=1.0cLow=
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Options and Futuresmin_value=1000fo
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Options and FuturesAppendix A - dat
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Options and FuturesNote that -1 mea
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Options and Futures16. The current
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Value at RiskIn finance, implicitly
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Chapter 11d1=stats.norm.pdf(0,0.1,0
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Chapter 11s=sp.arange(-10,z,delta)f
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Chapter 11ret=f(x)plt.plot(x,ret)x2
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Chapter 11z=norm.ppf(1-confidence_l
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Chapter 11#print(retNdays.head())po
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Chapter 11p =getData(ticker, begdat
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Chapter 11n=5000000#ret = random.no
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Chapter 11VaR based on sorted histo
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leftTail=int(n*(1-confidence_level)
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std=np.std(ret)#n_simulation=5000sp
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for i in np.arange(n):stock=tickers
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Chapter 11Again, we expect to see 2
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Chapter 11#sum=0.0for i in np.arang
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Chapter 11Estimation of an n-day Va
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Chapter 1110. When we estimate a Va
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Monte Carlo SimulationMonte Carlo S
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Chapter 12This program is equivalen
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Chapter 12Here, f(x) is the density
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Chapter 12import matplotlib.pyplot
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Chapter 12Using simulation to estim
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Chapter 12Generating random numbers
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Chapter 12#for i in range(len(nonSt
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Chapter 12The constraint specified
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Chapter 12Simulation of stock price
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Chapter 12Graphical presentation of
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Chapter 12y2=rho*x1+sp.sqrt(1-rho**
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dt=T/n_stepscall=sp.zeros([n_simula
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Chapter 12Based on the preceding re
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Chapter 12We have the following equ
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print("max NPV of project=",round(m
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Chapter 12One alternative is a so-c
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Chapter 12totalCost=salaryCost + ad
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[ 455 ]Chapter 12In other words, we
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Chapter 12Constructing an efficient
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Chapter 12The graph is shown here:I
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Chapter 12The following program ref
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Chapter 12On the other hand, if we
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4. To convert random numbers from a
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Credit Risk AnalysisThe objective o
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Chapter 136 A3 A- A- 1 17 Baa1 BBB+
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Chapter 13Source: Moody's (2007).No
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Chapter 13A secured debt is a debt
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If P is the default probability we
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14 B2/B 455.800 481.600 505.200 531
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Chapter 13Using the KMV model to es
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Chapter 13The following Python prog
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Chapter 13The related graph is show
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Chapter 13output.append(round(R,5))
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Chapter 13CDS P CDS P CDS P CDS P C
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8. What are uses of the term struct
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Exotic OptionsIn Chapter 10, Option
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Chapter 14x=40. # exercise priceT=6
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Chapter 14Here, call (T) is the cal
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Chapter 14v[i][j]=max(v1,v2)return
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Chapter 14n = mu.shape[0]Sigma_det
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Chapter 14First, we should study th
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Chapter 14sigma1=0.15sigma2=0.20pri
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Chapter 14The final price would be
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Chapter 14total+=sTprice_average=to
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Chapter 14#if sT<barrier:in_=True#p
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Chapter 14c=p4f.bs_call(s,x,T,r,sig
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Chapter 14The Python code for this
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Chapter 14If we use futures to hedg
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Chapter 14Here, T is the maturity d
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Chapter 14SummaryThe options we've
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Volatility, Implied Volatility, ARC
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IndexSymbols2-Step Approach 1522-st
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merging 228-234merging, based on da
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Monte Carlo Simulationabout 408, 42
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Python SimPy module 449QQuasi Monte
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