Description
The PPT on Exchange rate Modeling using Garch Model.
Exchange rate modeling – GARCH modeling
Problems with traditional models
? Homoskedasticity: The basic version of the least squares model assumes that the expected value of all error terms, when squared, is the same at any given point. This assumption is called homoskedasticity. Heteroskedasticity: Data in which the variances of the error terms are not equal, in which the error terms may reasonably be expected to be larger for some points or ranges of the data than for others, are said to suffer from heteroskedasticity. The standard errors and confidence intervals estimated by conventional procedures will be too narrow, giving a false sense of precision. The linear structural (and time series) models cannot explain a number of important features common to much financial data
? ? ? Leptokurtosis Volatility clustering or volatility pooling Leverage effects
?
?
Predicting the future volatility of exchange rates
? GARCH model stands for Generalized Autoregressive Conditional Heteroskedasticity ? The GARCH model is written as
? Divided exchange rates into two phases
? Jan 73 – March -93: Fixed exchange rate ? March-93 – August-2009: Managed floating exchange rate
Excel screenshots of the model
Date Apr-93 May-93 Jun-93 Jul-93 Aug-93 Sep-93 Oct-93 Nov-93 Dec-93 Jan-94 Feb-94 Mar-94 Apr-94 May-94 Jun-94 Jul-94 Aug-94 Sep-94 Oct-94 Nov-94 Dec-94 Jan-95 Feb-95 Mar-95 Rate 31.6 31.6 31.7 31.6 31.6 31.6 31.5 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.6 % change 0.00009 0.00176 -0.00215 0.00039 -0.00110 -0.00230 -0.00227 0.00021 0.00000 0.00028 -0.00109 -0.00074 -0.00051 0.00029 -0.00026 -0.00012 -0.00001 0.00001 0.00068 -0.00015 -0.00050 0.00019 0.00660 e_t -0.00220 -0.00053 -0.00444 -0.00190 -0.00339 -0.00459 -0.00456 -0.00208 -0.00229 -0.00201 -0.00338 -0.00303 -0.00280 -0.00200 -0.00255 -0.00241 -0.00230 -0.00228 -0.00161 -0.00244 -0.00279 -0.00210 0.00431 Var_t Log likelihood 0.00000 0.00003 0.00004 0.00005 0.00006 0.00006 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 12.18434453 9.796281819 9.934946299 9.656081578 9.398896333 9.332892116 9.535678476 9.556452425 9.592819618 9.491678136 9.506860501 9.524404352 9.587241792 9.566333989 9.577841418 9.588938041 9.594641251 9.63942568 9.598600868 9.562004211 9.60450641 9.385416109
Major finding
1973-1993
Forecasted Volatility Periodic variance Periodic stdev Long term stdev 0.00471 0.06865 0.92931
1973-1993
Forecasted Volatility Periodic variance Periodic stdev Long term stdev 0.00457 0.06757 0.78419
The variance and long term standard deviation regarding the exchange rate have decreased as India moved from a fixed exchange rate system to the managed float rate
Currency derivatives in India
? NSE launched its currency derivatives on Aug 29, 2008 ? BSE launched its currency derivatives on Oct 1, 2008 ? MCX received in-principal approval from SEBI for launch of currency derivatives on Aug 25, 2008
Using GARCH for pricing
? Most traditional models assume that the spot and futures returns follow a multivariate normal distribution with linear dependence. This assumption is at odds with numerous empirical studies, in which it has been shown that many financial asset returns are skewed, leptokurtic, and asymmetrically dependent. This can be explained by leverage effects and asymmetric responses to uncertainty. ? The GARCH model helps decompose the distribution into its marginal distributions and a copula, which can then be considered both separately and simultaneously. The marginal distributions can be any non-elliptical distributions, while the copula function describes the dependence structure between the spot and futures returns
doc_958217907.ppt
The PPT on Exchange rate Modeling using Garch Model.
Exchange rate modeling – GARCH modeling
Problems with traditional models
? Homoskedasticity: The basic version of the least squares model assumes that the expected value of all error terms, when squared, is the same at any given point. This assumption is called homoskedasticity. Heteroskedasticity: Data in which the variances of the error terms are not equal, in which the error terms may reasonably be expected to be larger for some points or ranges of the data than for others, are said to suffer from heteroskedasticity. The standard errors and confidence intervals estimated by conventional procedures will be too narrow, giving a false sense of precision. The linear structural (and time series) models cannot explain a number of important features common to much financial data
? ? ? Leptokurtosis Volatility clustering or volatility pooling Leverage effects
?
?
Predicting the future volatility of exchange rates
? GARCH model stands for Generalized Autoregressive Conditional Heteroskedasticity ? The GARCH model is written as
? Divided exchange rates into two phases
? Jan 73 – March -93: Fixed exchange rate ? March-93 – August-2009: Managed floating exchange rate
Excel screenshots of the model
Date Apr-93 May-93 Jun-93 Jul-93 Aug-93 Sep-93 Oct-93 Nov-93 Dec-93 Jan-94 Feb-94 Mar-94 Apr-94 May-94 Jun-94 Jul-94 Aug-94 Sep-94 Oct-94 Nov-94 Dec-94 Jan-95 Feb-95 Mar-95 Rate 31.6 31.6 31.7 31.6 31.6 31.6 31.5 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.6 % change 0.00009 0.00176 -0.00215 0.00039 -0.00110 -0.00230 -0.00227 0.00021 0.00000 0.00028 -0.00109 -0.00074 -0.00051 0.00029 -0.00026 -0.00012 -0.00001 0.00001 0.00068 -0.00015 -0.00050 0.00019 0.00660 e_t -0.00220 -0.00053 -0.00444 -0.00190 -0.00339 -0.00459 -0.00456 -0.00208 -0.00229 -0.00201 -0.00338 -0.00303 -0.00280 -0.00200 -0.00255 -0.00241 -0.00230 -0.00228 -0.00161 -0.00244 -0.00279 -0.00210 0.00431 Var_t Log likelihood 0.00000 0.00003 0.00004 0.00005 0.00006 0.00006 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 12.18434453 9.796281819 9.934946299 9.656081578 9.398896333 9.332892116 9.535678476 9.556452425 9.592819618 9.491678136 9.506860501 9.524404352 9.587241792 9.566333989 9.577841418 9.588938041 9.594641251 9.63942568 9.598600868 9.562004211 9.60450641 9.385416109
Major finding
1973-1993
Forecasted Volatility Periodic variance Periodic stdev Long term stdev 0.00471 0.06865 0.92931
1973-1993
Forecasted Volatility Periodic variance Periodic stdev Long term stdev 0.00457 0.06757 0.78419
The variance and long term standard deviation regarding the exchange rate have decreased as India moved from a fixed exchange rate system to the managed float rate
Currency derivatives in India
? NSE launched its currency derivatives on Aug 29, 2008 ? BSE launched its currency derivatives on Oct 1, 2008 ? MCX received in-principal approval from SEBI for launch of currency derivatives on Aug 25, 2008
Using GARCH for pricing
? Most traditional models assume that the spot and futures returns follow a multivariate normal distribution with linear dependence. This assumption is at odds with numerous empirical studies, in which it has been shown that many financial asset returns are skewed, leptokurtic, and asymmetrically dependent. This can be explained by leverage effects and asymmetric responses to uncertainty. ? The GARCH model helps decompose the distribution into its marginal distributions and a copula, which can then be considered both separately and simultaneously. The marginal distributions can be any non-elliptical distributions, while the copula function describes the dependence structure between the spot and futures returns
doc_958217907.ppt