Treasury Analytics INR VS US$

8/12/2019 Treasury Analytics INR VS US$

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To study Volatility between

INR and USD UsingHeteroskedastic Models

Submitted By:

Soumya Sreekumar12DM-145

Arifa Kazi12FN-024

Prakhar Saxena12DCP-080

Nikash Kumar12DCP-071

Tanuj Arora12DCP-117

Deepanshu Siddhanti12DCP-029


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Agenda

DataHistorical Exchange Rates for3 years (September 2010 -2013)

Tests for Stationarity If non stationary data exists, conversion to

stationary

Applying different ModelsARCH, GARCH, TARCH, E-GARCH and

PARCH


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Initial Approach

Exchange RatesTimeSeries Data

It can have VariableVariance andFar off Mean indicating

Non Stationarity

Thus, Cannot beModeled or Forecasted

as it is

Unit Root Testing inEviews determines Non

Stationarity

Conversion toStationarity by TakingLog Normal Returns


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Unit Root Tests

PhillipsPeron Test

Augmented Dickey-Fuller Test

P-value > 0.05means NullHypothesis cannot

be rejected.

Conclusion:Exchange Rate

data is non -stationary


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Conversion to Stationary Data

EviewsQuick TabGenerateSeries

Equation entered is:

usd_s = dlog(inr_usd) to giveContinuously Compounded Returns.

Applying Dickey Fuller Test

P-value < 0.05

means NullHypothesis can

be rejected

Conclusion:Exchange RateLog Return Data

is stationary


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ARMA Estimation Output

EviewsQuick TabEstimateEquation

Equation: Dlog(inr_usd) c ar(1) ma(1)

P-value < 0.05 meansNull Hypothesis can be

rejected

Conclusion:

Model is significant

ARYesterdays Pricedoes not have a

negative impact oncurrent price

MAYesterdaysVolatility has a positiveimpact on current price


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ARMA Graph


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Garch

AimForecast

variance based on

past information

All coefficients are

positive and

significant

Shocks to volatility

have a persistenteffecton the

conditional variance


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Tarch

AimTo check

asymmetric news

impact on the

volatility of

exchange rate

Gamma is negative

and significant

Bad news may not

increase volatility

Gamma 0 implies

asymmetric effect

of news is present

Dependent Variable: DLOG(INR_USD)Method: ML - ARCH (Marquardt) - Normal distributionDate: 09/11/13 Time: 20:48Sample (adjusted): 9/14/2010 9/10/2013Included observations: 763 after adjustmentsConvergence achieved after 15 iterationsMA Backcast: 9/13/2010Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-1) 2*(RESID(-1)


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E-Garch

Variable Coefficient Std. Error z-Statistic Prob.

C 0.000177 0.000175 1.010816 0.3121AR(1) -0.596517 0.143221 -4.165017 0.0000MA(1) 0.711246 0.124667 5.705174 0.0000

Variance Equation

C(4) -0.617559 0.154017 -4.009679 0.0001C(5) 0.232701 0.041022 5.672543 0.0000C(6) 0.076575 0.019992 3.830366 0.0001C(7) 0.958289 0.012939 74.05972 0.0000

R-squared 0.012717 Mean dependent var 0.000423Adjusted R-squared 0.004881 S.D. dependent var 0.005930S.E. of regression 0.005916 Akaike info criterion -7.672488Sum squared resid 0.026456 Schwarz criterion -7.629944Log likelihood 2934.054 Hannan-Quinn criter. -7.656108F-statistic 1.622938 Durbin-Watson stat 2.006895Prob(F-statistic) 0.137822

Inverted AR Roots -.60Inverted MA Roots -.71

AimTo study the

leverage effect of

news on exchange

rate

All coefficients are

positive

Bad news may not

have a strongerimpact than good

news.

Last periods

forecast has great

impact


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P-Garch


C 0.000249 0.000189 1.316457 0.1880AR(1) -0.589688 0.142506 -4.137998 0.0000MA(1) 0.707184 0.123404 5.730659 0.0000

Variance Equation

C(4) 0.000156 0.000248 0.626489 0.5310C(5) 0.122865 0.024157 5.086068 0.0000C(6) -0.371455 0.087933 -4.224301 0.0000C(7) 0.863090 0.025924 33.29256 0.0000C(8) 1.073143 0.287283 3.735495 0.0002



AimTo study the

asymmetric impact

of news on the

volatility of

exchange rate

Gamma is negative

and significant

Bad news has a

stronger impact onvolatility of

exchange rate than

good news.


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Component Garch

All the coefficients

are positive.

and are not

significant.

This means if there

is any bad news

and the rupee

depreciates the

change would notbe significantly

higher than when a

good news comes.

MA Backcast: 9/13/2010Presample variance: backcast (parameter = 0.7)Q = C(4) + C(5)*(Q(-1) - C(4)) + C(6)*(RESID(-1)^2 - GARCH(-1))

GARCH = Q + C(7) * (RESID(-1)^2 - Q(-1)) + C(8)*(GARCH(-1) - Q(-1))


C 0.000148 0.000186 0.797620 0.4251AR(1) -0.557471 0.176975 -3.150003 0.0016MA(1) 0.665888 0.162626 4.094604 0.0000

Variance Equation

C(4) 0.000171 0.000226 0.757949 0.4485C(5) 0.999509 0.000652 1532.768 0.0000C(6) 0.008344 0.019350 0.431191 0.6663C(7) 0.102803 0.026665 3.855385 0.0001C(8) 0.872383 0.031717 27.50560 0.0000




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Conclusions

Recent news affects volatility to agreater extent

Exchange rate volatility shows highpersistence

Asymmetric Effects of news onvolatility are present


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Thank you

Treasury Analytics INR VS US$

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