Comparing forecast performances among volatility estimation methods in the pricing of european type currency options of USD-TL and Euro-TL

Gozgor, Giray and Nokay, Pinar (2011): Comparing forecast performances among volatility estimation methods in the pricing of european type currency options of USD-TL and Euro-TL. Published in: Journal of Money, Investment and Banking No. 19 (15 January 2011): pp. 130-142.

Abstract

By using the daily values of USD-TL and Euro-TL denominated European call and put option contracts, which are traded in the over-the-counter market, this study investigates whether there is a significant difference among the premiums of the contracts forecasted by historical volatility, EWMA(l =0.94 andl =0.97), GARCH(1,1) and EGARCH( p, q) models. In order to test the significance of the difference among particular volatility series forecasted by these different methods, test techniques suggested by Diebold and Mariano (1995) and West (1996) are used. Accordingly, the findings indicate that the differences in the pricing of the USD-TL and Euro-TL denominated call-put option contracts are statistically significant for some volatility forecasting methods.

• Item Type: MPRA Paper
• Language: English
• Keywords: Option Pricing, European Type Vanilla Options, Historical Volatility, Volatility Estimation Models, Forecast Comparison
• Subjects: G - Financial Economics > G1 - General Financial Markets > G19 - Other

References

Akgiray, V., 1989. “Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts”, Journal of Business, 62, p. 55–80.

Andersen, T.G. and Bollerslev, T., 1998. “Answering the Skeptics: Yes. Standard Volatility Models Do Provide Accurate Forecasts”, International Economic Review, 39(4), p. 885–905.

Andersen, T.G., Bollerslev, T., and Lange, S., 1999. “Forecasting Financial Market Volatility: Sample Frequency vis-à-vis Forecast Horizon”, Journal of Empirical Finance 6(5), p. 457–477.

Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P., 2001. “The Distribution of Realized Exchange Rate Volatility”, Journal of American Statistical Association, 96(453), p. 42–57.

Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and Diebold, F.X., 2006. Volatility and Correlation Forecasting Handbook of Economic Forecasting, Amsterdam, Elsevier.

Balaban, E., Bayar, A. and Faff, R., 2006. “Forecasting Stock Market Volatility further International Evidence”. The European Journal of Finance, 122, p. 171-188.

Becker, R. and Clemens, A.E., 2008. “Are Combination Forecasts of S&P 500 Volatility Statistically Superior?” International Journal of Forecasting, 24, p. 122-133.

Benavides, G. and Capistran, C., 2009. “Forecasting Exchange Rate Volatility: The Superior Performance of Conditional Combinations of Time Series and Option Implied Forecasts”, Banco de Mexico Working Papers, 01-09.

Biger, N. and Hull, J.C., 1983. “The Valuation of Currency Options”, Financial Management, 12, p. 24-28.

Black, F. and Scholes, M., 1973. “The Pricing of Options and Corporate Liabilities” The Journal of Political Economy, 81(3), p. 637-659.

Bollerslev, T., 1986. “Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31, p. 307–328.

Caglayan, E. and Dayıoglu, T., 2009. “Forecasting Exchange Rate Returns Volatility with ARCH Models”, (In Turkish), Istanbul University Econometrics and Statistics E-Journal, 9(1), p. 1-16.

Chesney, M. and Scott, L., 1989. “Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and A Random Variance Model”, The Journal of Financial and Quantitative Analysis, 24(3), p. 267-284.

Clark, T.E. and West, K.D., 2007. “Approximately Normal Tests for Equal Predictive Accuracy in Nested Models”, Journal of Econometrics, 138(1), p. 291-311.

Cumby, R., Figlewski, S. and Hasbrouck, J., 1993. “Forecasting Volatilities and Correlations with E-GARCH Models”, Journal of Derivatives, 1, p. 51–63.

Diebold, F.X. and Mariano, R.S., 1995. “Comparing Predictive Accuracy”, Journal of Business and Economic Statistics, 13(3), p. 253-263.

Duan, J.C., 1995. “The GARCH Option Pricing Model”, Mathematical Finance, 5(1), p. 13-32.

Duan, J.C.and Wei, J., 1999. ”Pricing Foreign Currency and Cross Currency Options under GARCH”, Journal of Derivatives, 7(1), p. 51-63.

Dunis, C.L., Laws, J. and Chauvin, S., 2000. “The Use of Market Data and Model Combination to Improve Forecast Accuracy”, Liverpool Business School Working Paper.

Engle. R.F., 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation”, Econometrica, 50(4), p. 987–1007.

Engle. R.F., 2001. “The Use of ARCH/GARCH Models in Applied Econometrics”, Journal of Economic Perspective, 15(4), p. 157-168.

Figlewski, S., 1997. “Forecasting Volatility”, Financial Markets. Institutions and Instruments New York University Salomon Center Working Paper, 6(1), p. 1-88.

Garman, M. and Kohlhagen S., 1983. “Foreign Currency Option Values”, Journal of International Money and Finance, 2, p. 231-237.

Grabbe, O.J. 1983. “The Pricing of Call and Put Options on Foreign Exchange”, Journal of International Money and Finance, 2, p. 239-254.

Hansen, P. and Asger, R.L., 2005. “A Forecast Comparison of Volatility Models: Does Anything Beat A GARCH (1,1)?”, Journal of Applied Econometrics, 20, p. 873-889.

Herwartz. H. and Reimers, H.E., 2002. “Empirical Modeling of the DEM/USD and DEM/JPY Foreign Exchange Rate: Structural Shifts in GARCH-models and Their Implications”, Applied Stochastic Models in Business and Industry, 18, p. 3-22.

Heston, S.L., 1993, “A Closed Solution for Options with Stochastic Volatility with Application to Bond and Currency Options”, Review of Financial Studies 6(2), p. 327–343.

Hull, J.C. and White A., 1987. “The Pricing of Options on Assets with Stochastic Volatilities”, Journal of Finance, 2, p. 281-300.

Lopez, J.A., 2001. “Evaluating the Predictive Accuracy of Volatility Models”, Journal of Forecasting, 20(2), p. 87–109.

Merton, R.C., 1973. “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science, 4(1), p. 141-183.

Muradoglu, Y.G. and Kivilcim, M., 1996. “Efficiency of the Turkish Stock Market with Respect to Monetary Variables: A Cointegration Analysis”, European Journal of Operational Research, 90, p. 566-576.

Nelson, C.R. and Siegel, A.F., 1987. “Parsimonious Modeling Yield Curves”. Journal of Business, 60(4), p. 473-489.

Nelson, D.B., 1991. Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59(2), p. 347–370.

Pagan, A.R. and Schwert, G.W., 1990. “Alternative Models for Conditional Models for Conditional Stock Volatility”, Journal of Econometrics, 45(1), p. 267–290.

Pong, S., Shackleton, M.B., Taylor, S.J. and Xu, X., 2004. “Forecasting Sterling/dollar Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models”, Journal of Banking and Finance, 28, p. 2541–2563.

Ritchken, P. and Trevor, R., 1999. “Pricing Options under Generalized ARCH and Stochastic Volatility Processes”, Journal of Finance, 54(1), p. 377-402.

Schmitt, C., 1996. “Option Pricing Using E-GARCH Models”, ZEW-Centre for European Economic Research Discussion Paper, 96(20).

Stein, E.M. and Stein, C.J., 1991. “Stock Priced Distributions with Stochastic Volatility. An Analytical Approach”, Review of Financial Studies, 4(4), p. 727–752.

West. K.D., 1996. “Asymptotic Inference about Predictive Ability”, Econometrica, 64(5), p. 1067-1084.

Yavan, Z.A. and Aybar, C.B., 1998. “Volatility on ISE”, (In Turkish), ISE Review, 2(6), p. 35- 47.

Zivot, E.D. and Andwers, W.K., 1992. “Further Evidence on the Great Crash the Oil Price Shock and Unit Root Hypothesis”, Journal of Business and Economic Statistics, 10(3), p. 251- 270.