Ekstrem değerler teorisi ve Monte Carlo simülasyonu: Gelişen ülke döviz kurları üzerine bir uygulama

Abstract

Bu çalışmada Brezilya, Meksika, G. Kore, Tayvan, Hindistan, Tayland, Türkiye ve G. Afrika’dan oluşan 8 gelişen ülkenin para birimlerinin ekstrem finansal koşulların söz konusu olması durumunda maruz kalabileceği maksimum kayıp tutarları hesaplanmıştır. Hesaplamalarda ekstrem değerler teorisinden (Extreme value theory) yararlanılmış ve farklı döviz pozisyonlarını dikkate almak amacıyla hem aşağı hem de yukarı yönlü piyasa riski (downside and upside market risk) üzerinde durulmuştur. Çalışmada finansal risk yönetimi açısından bir diğer önemli gösterge olan beklenen kayıp tutarları (Expected Shortfall, ES) da hesaplanmıştır. Çalışma bulguları ilgili ülkelerin döviz piyasalarında ekstrem durumların gerçekleşmesi durumunda hem kısa hem de uzun pozisyonlar için en yüksek kayıp tutarlarının sırasıyla Brezilya Reali ve G.Afrika Randı; en düşük kayıp tutarlarının ise Yeni Tayvan Doları, Tayland Bahtı ve Hindistan Rupisinde gerçekleşebileceğini göstermektedir. ES değerlerinin de benzer bulgulara işaret ettiği görülmüştür. Çalışmada, normal piyasa koşullarındaki kayıp tutarlarını temsilen Monte Carlo simülasyonuna dayalı finansal risk analizlerine de yer verilmiştir.

Keywords

• Beklenen kayıp tutarları,Döviz kurları,Ekstrem değerler teorisi,Monte Carlo simülasyonu,Riske maruz değer

Extreme value theory and Monte Carlo simulation: An application to emerging markets exchange rates

Abstract

In this study, the maximum amount of losses to which the emerging market currencies including Brazilian Real, Mexico Peso, South Korean Won, New Taiwan Dollar, Indian Rupee, Thailand Bahd, Turkish Lira and South African Rand can be exposed due to extreme financial conditions is measured by using value-at-risk based on extreme value theory (EVT-VaR). In order to take into account the different trading positions (i.e. long and short ones) both upside and downside market risks are considered. In all cases expected shortfall is also calculated. The findings based on EVT-VaR show that in the case of extreme financial conditions in foreign exchange markets of the countries concerned, the highest losses for both short and long positions are in Brazilian Real and south African Rand; while the lowest losses are in New Taiwan Dollar, Thai Baht and Indian Rupee. In all cases ES also indicates the similar results. Lastly, for comparative analyses, the study also includes risk analyzes based on Monte Carlo simulation, representing losses in normal market conditions.

Keywords

• Expected shortfall,Exchange rates,Extreme value theory,Monte Carlo simulation,Value-at-risk

References

1. [1] T. Angelidis, A. Benos, S. Degiannakis, 2004, The Use of GARCH models in VaR estimation, Statistical Methodology,1, 105-128.
2. [2] P. Abad, S. Benito, C. Lopez, 2014, A comprehensive review of value-at-risk methodologies, The Spanish Review of Financial Economics, 12 (1), 15-32.
3. [3] P.F. Diamandis, A.A. Drakos, G.P. Kouretas, L. Zarangas, 2011, value-at-risk for long and short trading positions: Evidence from developed and emerging equity markets, International Review of Financial Analysis, 20,165-176.
4. [4] P. De Grauwe, 2008, The banking crisis: Causes, consequences and remedies, Centre for European Policy Studies, 178, 1-12.
5. [5] L. T. Orlowski, 2012, Financial crisis and extreme market risks: Evidence from Europe, Review of Financial Economics, 21, 120-130.
6. [6] S.B. Muela, C.L. Martin, R.A. Sanz, 2017, An application of extreme value theory in estimating liquidity risk, European Research on Management and Business Economics, 23 (3), 157-164.
7. [7] A.J. McNeil, R. Frey, 2000, Estimation of tail-related risk measures for heteroscedastic financial time series : An extreme value approach, Journal of Empirical Finance, 7, 271-300.
8. [8] M. Gilli, E. Kellezi, 2006, An application of extreme value theory for measuring financial risk, Computational Economics, 27, 207–228.

9. [9] A. Ghorbel, A. Trabelsi, 2008, Predictive performance of conditional extreme value theory in value-at-risk estimation, International Journal of Monetary Economics and Finance, 1(2), 121-148.
10. [10] V. Marimoutou, B. Raggad, A. Trabelsi, 2009, Extreme value theory and value-at-risk: Application to oil market, Energy Economics, 31, 519-530.
11. [11] D.N. Dimitrakopoulos, M.G. Kavussanos, S.I. Spyrou, 2010, Value-at-risk models for volatile emerging markets equity portfolios, The Quarterly Review of Economics and Finance, 50 (4), 515-526.
12. [12] A. Cifter, 2011, Value-at-risk estimation with wavelet–based extreme value theory: Evidence from emerging markets, Physica A, 390, 2356-2367.
13. [13] R. Jesús, E. Ortiz, A. Cabello, 2013, Long run peso/dollar exchange rates and extreme value behavior: Value-at-risk modeling, The North American Journal of Economics and Finance, 24, 139-152.
14. [14] E. Altun, 2014, Uç değerler teorisi ve riske maruz değer, Yüksek Lisans Tezi, http://www.openaccess.hacettepe.edu.tr:8080/xmlui/bitstream/handle/11655/2115.
15. [15] M. Karmakar, G.K. Shukla, 2015, Managing extreme risk in some major stock markets: An extreme value approach, International Review of Economics And Finance, 35, 1-25.
16. [16] G. Trzpiot, J. Majewska, 2010, Estimation of value-at-risk: Extreme value and robust approaches, Operations Research and Decision, 20 (1), 131-143.
17. [17] H.N.E. Byström, 2004, Managing extreme risks in tranguil and volatile markets using conditional extreme value theory, International Review of Financial Anaysis, 13, 133-152.
18. [18] R. Gençay, F. Selçuk, 2004, Extreme value theory and value-at-risk: Relative performance in emerging markets, International Journal of Forecasting, 20,287-303.
19. [19] Z. Wang, W. Wu, C. Chen, Y. Zhou, 2010, The exchange rate risk of Chinese yuan: Using VaR and ES based on extreme value theory, Journal of Applied Statistics, 37 (2), 265-282.
20. [20] G. Liao, T-Z. Pan, L-F. Chang, S-C. Huang, C-F. Wu, 2012, Portfolio value-at-risk by Bayesian conditional EVT-copula models: taking an Asian index portfolio for example, Journal of Statistics and Management Systems, 15 (2), 345-367.
21. [21] A. Goncu, A.K. Akgul, O. Imamoğlu, M. Tiryakioğlu, M. Tiryakioğlu, 2012, An analysis of the extreme returns distribution: The case of the Istanbul Stock Exchange, Applied Financial Economics, 22(9), 723-732.
22. [22] A. Çifter, A. Özün, S. Yılmazer, 2007a, Beklenen kuyruk kaybı ve genelleştirilmiş pareto dağılımı ile riske maruz değer öngörüsü: Faiz oranları üzerine bir uygulama, Bankacılar Dergisi, 60, 3-16.
23. [23] A. Çifter, A. Özün, S. Yılmazer, 2007b, Geriye dönük testlerin karşılaştırmalı analizi: Döviz kuru üzerine bir uygulama, Bankacılar Dergisi, 62, 27-43.
24. [24] E.M. Iglesias, M. Dolores, L. Varela, 2012, Extreme movements of the main stocks traded in the Eurozone: An analysis by sectors in the 2000's decade, Applied Financial Economics, 22 (24), 2085-2100.
25. [25] E.M. Iglesias, 2012, An analysis of extreme movements of exchange rates of the main currencies traded in the foreign exchange market, Applied Economics, 44, 4631-4637.
26. [26] A. Assaf, 2009, Extreme observations and risk assessment in the equity markets of MENA region: Tail measures and value-at-risk, International Review of Financial Analysis, 18, 109-116.
27. [27] E.M. Iglesias, 2015, Value-at-risk and expected shortfall of firms in the main European Union stock market ındexes: A detailed analysis by economic sectors and geographical situation, Economic Modelling, 50, 1-8.
28. [28] L. Kalyvas, C. Siriopoulos, N. Dritsakis, 2004, Reaching extreme events with conditional and unconditional models, WSEAS Transactions on Business and Economics, 1 (1), 156-162.
29. [29] C. Payaslioglu, 2009, A tail index tour across foreign exchange rate regimes in Turkey, Applied Economics , 41 (3),381-397.
30. [30] Y. Bensalah, 2000, Steps in applying extreme value theory to finance: A review, Bank of Canada, Working Paper 2000-20. Research and Risk management Section, Financial Markets Department.
31. [31] F. Ren, D.E. Giles, 2010, Extreme value analysis of daily Canadian crude oil prices, Applied Financial Economics, 20 (12), 941-954.
32. [32] T. Fretheim, G. Kristiansen, 2015, Commodity market risk from 1995 to 2013: An extreme value theory approach, Applied Economics, 47 (26), 2768-2782.
33. [33] A.A. Soyalp, E. Nevruz, U. Karabey, 2013, Gelişmekte olan bazı piyasalarda finansal risklerin uç değer kuramı ile ölçülmesi, İstatistikçiler Dergisi: İstatistik & Aktüerya, 6, 86-95.
34. [34] N. Çelik, M.F. Kaya, 2010, Uç değerler yöntemi ile riske maruz değer’in tahmini ve İstanbul Menkul Kıymetler Borsası üzerine bir uygulama, Bankacılık ve Sigortacılık Araştırmaları Dergisi, 1(1), 19-32.
35. [35] A. Arik, B. Bulut, M. Sucu, 2013, Finansal risklerin uç değer kuramı ile ölçülmesi, Bilim ve Teknoloji Dergisi A - Uygulamalı Bilimler ve Mühendislik, 14 (2), 119-134.
36. [36] E. Başçı, H. Kara, 2011, Finansal istikrar ve para politikası, İktisat, İşletme ve Finans Dergisi, 26 (302), 9-25.
37. [37] A.H. Kara, 2012, Küresel kriz sonrası para politikası, İktisat, İşletme ve Finans Dergisi, 27, (315), 9-36.
38. [38] W. Chkili, C. Aloui, D.K. Nguyen, 2012, Asymmetric effects and long memory in dynamic volatility relationships between stock returns and exchange rates, Journal of International Financial Markets, Institutions and Money, 22, 738–757.
39. [39] Y. Fan, Y.J. Zhang, H.T. Tsai, Y.M. Wei, 2008, Estimating ‘value-at-risk’ of crude oil price and its spillover effect using the GED–GARCH approach, Energy Economics, 30 (6), 3156-3171.
40. [40] P. Giot, S. Laurent, 2003, Value-at-risk for long and short positions, Journal of Applied Econometrics, 18, 641–664.
41. [41] W. Chkili, S. Hammoudeh, D.K. Nguyen, D.K, 2014, Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory, Energy Economics, 41, 1-18.
42. [42] C. Aloui, S. Mabrouk, 2010, Value-at-risk estimations of energy commodities via long memory, asymmetry and fat-tailed GARCH models, Energy Policy, 38, 2326–2339.
43. [43] P. Artzner, J. Delbaen, M. Eber, D. Heath, 1997, Thinking coherently, Risk, 10 (11), 68–71.
44. [44] P. Artzner, J. Delbaen, M. Eber, D. Heath, 1999, Coherent measures of risk, Mathematical Finance, 9 (3), 203–228.
45. [45] Y. Yamai, T. Yoshiba, 2005, Value-at-risk versus expected shortfall: A practical perspective, Journal of Banking & Finance, 29, 997-1015.
46. [46] A.F. Rossignolo, M.D. Fethi, M. Shaban, 2012, Value-at-risk models and basel capital charges: evidence from emerging and frontier stock markets, Journal of Financial Stability, 8(4), 303-319.
47. [47] S. Basak, A. Shapiro, 2001, Value-at-risk-based risk management: Optimal policies and asset prices, The Review of Financial Studies, 14(2), 371–405.
48. [48] F.M. Longin, 2000, From value-at-risk to stres testing: The extreme value approach, Journal of Banking & Finance, 24, 1097-1130.
49. [49] A.K. Singh, D.E. Allen, P.J. Robert, 2013, Extreme market risk and extreme value theory, Mathematics and Computers in Simulation, 94, 310-328.
50. [50] L. Kourouma, D. Dupre, G Sanfilippo, O. Taramasco, 2011, Extreme value-at-risk and expected shortfall during financial crisis. Available at SSRN: https://ssrn.com/abstract=1744091.
51. [51] B.M. Hill, 1975, A simple general approach to inference about the tail of a distribution, Annals of Statistics, 3, 1163-1174.
52. [52] S.N. Neftci, 2000, Value-at-risk calculations, extreme events, and tail estimation, The Journal of Derivatives, 7 (3) , 23-38.
53. [53] P. Blum, M. Dacorogna, 2003, Extreme forex moves, RISK, Februray, 63-67.
54. [54] M. Dacorogna, R. Gencay, U. Muller, R. Olsen, O. Pictet, 2001, An introduction to high frequency finance, Academic Press, California.
55. [55] A. Ferreira, L. de Haan, L. Peng, 2003, On optimising the estimation of high quantiles of a probability distribution, Statistics, 37, 401–434.
56. [56] M. Loretan, P.C.B. Philips, 1994, Testing the covariance stationarity of heavy tailed time series: An overview of the theory with applications to several financial datasets, Journal of Empirical Finance, 1 (2), 211–248, 1994.
57. [57] W.H. DuMouchel, 1983, Estimating the stable index α in order to measure tail thickness: A critique, The Annals of Statistics, 11 (4), 1019–1031, 1983.
58. [58] J. Gavin, 2000, Extreme value theory–an empirical analysis of equity risk, Quantative Risk: Models & Statistics UBS Warburg, August, 1-9.
59. [59] T.G. Bali, S.N. Neftci, 2003, Disturbing extremal behavior of spot rate dynamics, Journal of Emprical Finance, 10, 455-477.
60. [60] E.M. Iglesias, M.D.L. Varela, 2012, Extreme movements of the main stocks traded in the Eurozone: An analysis by sectors in the 2000's decade, Applied Financial Economics, 22:24, 2085-2100.
61. [61] A. Ghorbel, S. Souilmi, 2014, Risk measurement in commodities markets using conditional extreme value theory, International Journal of Econometrics and Financial Management, 2(5), 188-205.
62. [62] J. Daniessson, C.G. de Vries, 2000, Value-at-risk and extreme returns, Annales d'Économie et de Statistique, 60, 239-270.
63. [63] S.P. Peterson, 2012, Models of stock price Dynamics in ınvestment theory and risk management, John Wiley & Sons, Inc., Hoboken, New Jersey, USA.
64. [64] J.B. Su, 2014, Emprical analysis of long memory, leverage, and distribution effects for stock market risk estimates, North American Journal of Economics and Finance, 30, 1-39.