Modeling of Stochastic Volatility  to Validate IDR Anchor Currency

Didit Budi Nugroho; Tundjung Mahatma; Yulius Pratomo

doi:10.22146/gamaijb.26006

Modeling of Stochastic Volatility to Validate IDR Anchor Currency

Didit Budi Nugroho, Tundjung Mahatma, Yulius Pratomo

(Submitted 16 June 2017)

(Published 30 August 2018)

Abstract

This study aims to assess the performance of stochastic volatility models for their estimation of foreign exchange rate returns' volatility using daily data from Bank Indonesia (BI). The model is then applied to validate the anchor currency of Indonesian rupiah (IDR). Two stylized facts are incorporated into the models: A correlation between the previous returns and their conditional variance, and return errors following four different error distributions namely Normal, Student-t, non-central Student-t, and generalized hyperbolic skew Student-t. The analysis is based on the application of daily returns data from nine foreign currency selling rates to IDR from 2010 to 2015, including the AUD, CHF, CNY, EUR, GBP, JPY, MYR, SGD, and USD. The main results are: (1) Mixed evidence of positive and negative relationships between the return and its variance were found, especially significant correlations being found for the IDR/AUD, IDR/CHF, IDR/JPY, IDR/SGD, and IDR/USD returns series; (2) the model with the generalized hyperbolic skew Student's t-distribution specification for the returns error provides the best performance; and (3) anchoring the IDR to established hard currencies is more appropriate than anchoring it to other currencies.

Keywords

asymmetric effect, Bayesian inference, currency exchange rates, generalized Student-t, stochastic volatility

Full Text: PDF

DOI: 10.22146/gamaijb.26006

References

Abdalla, S. Z. S. and P. Winker. 2012. Modelling stock market volatility Using univariate GARCH models: Evidence from Sudan and Egypt. International Journal of Economics and Finance 4 (8): 161-176.
Andersson, H., and T. Britton. 2000. Stochastic Epidemic Models and Their Statistical Analysis. New York: Springer-Verlag.
Black, F. 1976. Studies of stock market volatility changes. Proceedings of the 1976 Meetings of the Business and Economic Statistics. American Statistical Association: 177-181.
Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31 (3): 307-327.
Chen, M.-H., and Q-M. Shao. 1999. Monte carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8 (1): 69.
Cont, R. 2007. Volatility clustering in financial markets: Empirical facts and agent-based models. In G. Teyssière and A. P. Kirman (Eds.). Long Memory in Economics. Berlin: Springer, pp.289-309.
Conway, E. 2009. UN wants new global currency to replace dollar. [online] Available at: <https://www.telegraph.co.uk/finance/currency/6152204/UN-wants-new-global-currency-to-replace-dollar.html> [Accessed 24 Nov. 2017].
Corsetti, G., P. Pesenti, and N. Roubini. 1999. What caused the Asian currency and financial crisis? Japan and the World Economy 11 (3): 305-373.
Degiannakis, S. and C. Floros. 2015. Modelling and Forecasting High Frequency Financial data. London: Palgrave Macmillan UK.
Dickey, D. A., and W. A. Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (366): 427.
Eichengreen, B. 2005. Sterling's Past, Dollar's Future: Historical Perspectives on Reserve Currency Competition. [online] Cambridge, MA. Available at: <http://www.nber.org/papers/w11336.pdf>.
Engle, R. F. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 (4): 987-1007.
Gelfand, A. E., and D. K. Dey. 1994. Bayesian model choice: Asymptotics and exact calculations. Journal of the Royal Statistical Society. Series B (Methodological), .
Goyal, A. 2017. Intervention and signaling: Interaction between central banks and FX markets in an emerging market. The Singapore Economic Review 62 (1): 193-225.
Harvey, A. C., and N. Shephard. 1996. Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business and Economic Statistics 14 (4): 429.
Ho, K.-Y., Y. Shi, and Z. Zhang. 2017. Does news matter in China's foreign exchange market? Chinese RMB volatility and public information arrivals. International Review of Economics and Finance 52: 302-321.
IMF Website. 2016. IMF Adds Chinese Renminbi to Special Drawing Rights Basket. [online]. Available at: <http://www.imf.org/en/News/Articles/2016/09/29/AM16-NA093016IMF-Adds-Chinese-Renminbi-to-Special-Drawing-Rights-Basket> [Accessed 15 Nov. 2017].
Kass, R. E., and A. E. Raftery. 1995. Bayes factors. Journal of the American Statistical Association. [online] 90(430), pp.773-795. Available at: <http://www.jstor.org/stable/2291091?origin=crossref>.
Kim, S. -J. 2015. Australian gollar carry trades: Time varying probabilities and determinants. International Review of Financial Analysis 40: 64-75.
Kompas. 2015. Importir Kena Dampak Rupiah (March) (14): 1.
Laopodis, N. T. 2005. Feedback trading and autocorrelation interactions in the foreign exchange market: Further evidence. Economic Modelling 22 (5): 811-827.
Lee, S.-Y., and X-Y. Song. 2008. Bayesian model comparison of structural equation models. Random Effect and Latent Variable Model Selection. New York: Springer Science and Business Media: 121-150.
Los, C. A. 2003. Financial Market Risk: Measurement and Analysis. London: Routledge.
Low, C. 2004. The fear and exuberance from implied volatility of SandP 100 index options. The Journal of Business 77 (3): 527-546.
Moon, W., 2007. A case for a coordinated basket for Asian countries. In A Basket Currency for Asia 124-141. New York: Routledge
Moreno, E., F. J. Girón, and G. Casella. 2010. Consistency of objective Bayes factors as the model dimension grows. Annals of Statistics 38 (4): 1937-1952.
Mukhlis, I., 2011. Analisis volatilitas nilai tukar mata uang rupiah terhadap dolar. Journal of Indonesian Applied Economics, 5(2), pp.178-182.
Nugroho, D.B. and Morimoto, T., 2014. Realized non-linear stochastic volatility models with asymmetric effects and generalized Student's t-distributions. Journal of the Japan Statistical Society, 44(1), pp.83-118.
Nugroho, D.B. and Morimoto, T., 2015. Estimation of realized stochastic volatility models using Hamiltonian Monte Carlo-Based methods. Computational Statistics, 30(2), pp.491-516.
Nugroho, D.B. and Morimoto, T., 2016. Box-Cox realized asymmetric stochastic volatility models with generalized Student's t -error distributions. Journal of Applied Statistics, 43(10), pp.1906-1927.
Nugroho, D.B. and Susanto, B., 2017. Volatility modeling for IDR exchange rate through APARCH model with student-t distribution. In: AIP Conference Proceedings. AIP Publishing LLC, p.40005.
Nugroho, D.B., Susanto, B. and Pratama, S.R., 2017. Estimation of exchange rate volatility using APARCH-type models: A case study of Indonesia (2010-2015). Jurnal Ekonomi dan Ekonomi Studi Pembangunan, 9(1), pp.65-75.
Ogawa, E. and Shimizu, J., 2009. Currency denomination in Asian Bond Markets. In: K. Hamada, B. Reszat and U. Volz, eds., Towards monetary and financial integration in East Asia. Cheltenham: Edward Elgar Publishing Limited.
Poon, S.-H., 2005. A practical guide to forecasting financial market volatility. Chichester: John Wiley and Sons.
Saadah, S. and Panjaitan, Y., 2016. The green shoe option's effectiveness at stabilizing the IPO's stock price on the Indonesian Stock Exchange (2000-2013). Gadjah Mada International Journal of Business, 18(1), p.71.
Salim, F.C., Nugroho, D.B. and Susanto, B., 2016. Model volatilitas GARCH(1,1) dengan error Student-t untuk kurs beli EUR dan JPY terhadap IDR. Jurnal MIPA, 39(1), pp.63-69.
Salvatore, D., 2013. International economics. 11th ed. New York: John Wiley and Sons.
Saputri, E.D., Nugroho, D.B. and Setiawan, A., 2016. Model volatilitas ARCH(1) dengan return error berdistribusi skewed Student-t. Jurnal MIPA, 39(1), pp.78-84.
Sekerke, M., 2015. Bayesian risk management: A guide to model risk and sequential learning in financial markets. New York: John Wiley and Sons.
Sumiyana, S., 2007. Behavior of stock price variability over trading and nontrading periods, and daily return volatility. Gadjah Mada International Journal of Business, 9(3), pp.409-453.
Tan, Z., 2008. Monte Carlo integration with Markov chain. Journal of Statistical Planning and Inference 138 (7): 1967-1980.
Taylor, S. J. 1982. Financial returns modelled by the product of two stochastic processes —A study of the daily sugar prices 1961-75. In N. Shephard (Ed.), Stochastic volatility: Selected readings: 60-82. Oxford University Press.
Taylor, S. J. 1994. Modeling stochastic volatility: A review and comparative study. Mathematical Finance 4 (2): 183-204.
Triady, M. S., R. Kurniasari, A. F. Utami, and M. I. Sofyan. 2016. Investigation of leverage effect in Indonesian Stock Market. International Journal of Economics and Management 10 (S1): 1-17.
Tsay, R. S. 2010. Analysis of Financial Time Series (3rd ed.). New York: John Wiley and Sons.
Tsiotas, G. 2012. On generalised asymmetric stochastic volatility models. Computational Statistics and Data Analysis 56 (1): 151-172.
van der Ploeg, A. P. C. 2006. Stochastic Volatility and the Pricing of Financial Derivatives. Amsterdam: Rozenberg Publishers.
Wang, M., and Y. Maruyama. 2016. Consistency of Bayes factor for nonnested model selection when the model dimension grows. Bernoulli [online] 22 (4): 2080-2100. Available at: <http://projecteuclid.org/euclid.bj/1462297675>.
XE Website. 2017. IDR - Indonesian Rupiah. [online]. Available at: <http://www.xe.com/currency/idr-indonesian-rupiah> [Accessed 6 Nov. 2017].
Yu, J., Z. Yang, and X. Zhang. 2006. A class of nonlinear stochastic volatility models and its implications for pricing currency options. Computational Statistics and Data Analysis 51 (4): 2218-2231.

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