MIT18_S096F13_CaseStudy4.pdf - Volatility Modeling Case Study 4 Dr Kempthorne October 8 2013 Contents 1 Volatility Modeling of Exchange Rate Returns 1.1

MIT18_S096F13_CaseStudy4.pdf - Volatility Modeling Case...

This preview shows page 1 - 5 out of 32 pages.

Volatility Modeling: Case Study 4Dr. KempthorneOctober 8, 2013Contents1Volatility Modeling of Exchange Rate Returns21.1Load libraries and Federal Reserve FX Data. . . . . . . . . . .21.2Geometric Brownian Motion Model (two time scales). . . . . . .31.3Time Dependence in Squared-Returns. . . . . . . . . . . . . . .101.4Gaussian ARCH and GARCH Models. . . . . . . . . . . . . . .111.5GARCH(1,1) Models with t Distributions. . . . . . . . . . . . .181
Background image
1Volatility Modeling of Exchange Rate Returns1.1Load libraries and Federal Reserve FX Data> # 0.1 Install/load libraries> source(file="fm_casestudy_0_InstallOrLoadLibraries.r")> library("zoo")> # 0.2 Load R workspace created by script fm_casestudy_fx_1.r> load(file="fm_casestudy_fx_1.Rdata")> # 1.0 Extract time series matrix of exchange rates for symbols given by list.symbol0 ---->> list.symbol0<-c("DEXCHUS", "DEXJPUS", "DEXKOUS", "DEXMAUS",+"DEXUSEU", "DEXUSUK", "DEXTHUS", "DEXSZUS")> fxrates000<-fred.fxrates.00[,list.symbol0]> dim(fxrates000)[1] 37098> head(fxrates000)DEXCHUS DEXJPUS DEXKOUS DEXMAUS DEXUSEU DEXUSUK DEXTHUS DEXSZUS1999-01-048.2793112.151187.53.81.18121.658136.201.36661999-01-058.2795111.151166.03.81.17601.656636.181.36941999-01-068.2795112.781160.03.81.16361.654736.501.38521999-01-078.2798111.691151.03.81.16721.649536.301.38631999-01-088.2796111.521174.03.81.15541.640536.451.39701999-01-118.2797108.831175.03.81.15341.637536.281.3963> tail(fxrates000)DEXCHUS DEXJPUS DEXKOUS DEXMAUS DEXUSEU DEXUSUK DEXTHUS DEXSZUS2013-09-206.121099.38 1076.023.16401.35221.602131.040.91042013-09-236.284298.76 1073.903.19901.35201.606631.180.91002013-09-246.120898.76 1074.353.21501.34901.600631.270.91142013-09-256.119098.62 1076.423.22101.35361.608031.220.90822013-09-266.119498.95 1075.203.21451.34841.601231.160.91052013-09-276.117998.30 1074.383.22601.35371.613531.280.9050>> # Print symbol/description/units of these rates from data framefred.fxrates.doc> options(width=120)> print(fred.fxrates.doc[match(list.symbol0, fred.fxrates.doc$symbol),+c("symbol0", "fx.desc", "fx.units")])symbol0fx.descfx.units3DEXCHUSChina / U.S. Foreign Exchange RateChinese Yuan to1 U.S. $7DEXJPUSJapan / U.S. Foreign Exchange RateJapanese Yen to1 U.S. $2
Background image
8DEXKOUS South Korea / U.S. Foreign Exchange RateSouth Korean Won to1 U.S. $9DEXMAUSMalaysia / U.S. Foreign Exchange Rate Malaysian Ringgit to1 U.S. $20 DEXUSEUU.S. / Euro Foreign Exchange RateU.S. $ to1 Euro22 DEXUSUKU.S. / U.K. Foreign Exchange RateU.S. $ to1 British Pound18 DEXTHUSThailand / U.S. Foreign Exchange RateThai Baht to1 U.S. $16 DEXSZUS Switzerland / U.S. Foreign Exchange RateSwiss Francs to1 U.S. $> source("test_vol1b.r")>1.2Geometric Brownian Motion Model (two time scales)Case 1: EUR/USD Exchange Rate ReturnsThe objectfx.USEUis a“zoo”time series object of daily US/Euro exchangerates from 1999 to 2013. The functionfcn.itsreturnscomputes log returns ofirregular daily time series and provides time information including the numberof days in the return, the starting date of the return, the ending date of thereturn, and the day-of-week of the ending date.> par(mfcol=c(2,1))> plot(fx.USEU)> fx.USEU.itsreturns<-fcn.itsreturns(fx.USEU)> head(fx.USEU.itsreturns)ret ndays date.end date.start dayofweek1999-01-05 -0.0044120211105961059531999-01-06 -0.0106002021105971059641999-01-070.0030890711105981059751999-01-08 -0.0101611141105991059861999-01-11 -0.0017325023106021059921999-01-120.001213067110603106023> plot(zoo(fx.USEU.itsreturns[,"ret"], order.by=as.Date(fx.USEU.itsreturns[,"date.end"])),+ ylab="Return")3
Background image
Jan 04 1999Jul 01 2002Jan 03 2006Jul 01 2009Jan 02 20130.81.21.6fx.USEU200020052010-0.020.02IndexReturnThe next page presents two plots:A histogram of the returns is created and the Gaussian/normal densitycorresponding to the maximum-likelihood fit is drawn.
Background image
Image of page 5

You've reached the end of your free preview.

Want to read all 32 pages?

  • Spring '17
  • Jim Angel

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors