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Analysis of the Exchange Rate and Pricing Foreign Currency Options on the Croatian Market: the NGARCH Model as an Alternative to the Black-Scholes Model

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  • Petra Posedel

    (Faculty of Economic and Business, Zagreb)

Abstract

The interest of professional investors in financial derivatives on the Croatian market is steadily increasing and trading is expected to start after the establishment of the legal framework. The quantification of the fair price of such financial instruments is therefore becoming increasingly important. Once the derivatives market is formed, the use of the Black-Scholes option pricing model is also expected. However, contrary to the assumptions of the Black-Scholes model, research in the field of option markets worldwide suggests that the volatility of the time-series returns is not constant over time. The present study analyzes the implications of volatility that changes over time for option pricing. The nonlinear-in-mean asymmetric GARCH model that reflects asymmetry in the distribution of returns and the correlation between returns and variance is recommended. For the purpose of illustration, we use the NGARCH model for the pricing of foreign currency options. Possible prices for such options having different strikes and maturities are then determined using Monte Carlo simulations. The improvement provided by the NGARCH model is that the option price is a function of the risk premium embedded in the underlying asset. This contrasts with the standard preference-free option pricing result that is obtained in the Black-Scholes model.

Suggested Citation

  • Petra Posedel, 2006. "Analysis of the Exchange Rate and Pricing Foreign Currency Options on the Croatian Market: the NGARCH Model as an Alternative to the Black-Scholes Model," Financial Theory and Practice, Institute of Public Finance, vol. 30(4), pages 347-368.
  • Handle: RePEc:ipf:finteo:v:30:y:2006:i:4:p:347-368
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    File URL: http://www.ijf.hr/eng/FTP/2006/4/posedel.pdf
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    References listed on IDEAS

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    1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    4. Kuldeep Shastri & Kulpatra Wethyavivorn, 1987. "The Valuation Of Currency Options For Alternate Stochastic Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(4), pages 283-293, December.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    7. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
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    Cited by:

    1. Kovačić, Zlatko, 2007. "Forecasting volatility: Evidence from the Macedonian stock exchange," MPRA Paper 5319, University Library of Munich, Germany.

    More about this item

    Keywords

    Black-Scholes model; NGARCH model; heteroscedasticity; volatility; risk premium; risk-neutral measure; no arbitrage; Monte Carlo simulations.;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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