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Liburkina L. M.

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The Definition of Risks of Hryvnia Currency Options Using the Garman–Kohlhagen Model
Yakubets A. O., Lukianenko I. H.

Yakubets, Andrii O., and Lukianenko, Iryna H. (2026) “The Definition of Risks of Hryvnia Currency Options Using the Garman–Kohlhagen Model.” Business Inform 3:417–424.
https://doi.org/10.32983/2222-4459-2026-3-417-424

Section: Finance, Money Circulation and Credit

Article is written in Ukrainian
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UDC 336.76

Abstract:
The article provides a comprehensive study of the theoretical foundations and practical aspects of applying the Garman – Kohlhagen model to assess the fair value and risks of hryvnia currency options in the context of the functioning of the financial market in Ukraine. The relevance of the study is due to the high volatility of the national currency, the significant difference in interest rates between the hryvnia and foreign currencies, as well as the growing role of derivative financial instruments in the system of managing market risks by banks and State financial institutions. In conditions of macroeconomic instability, the use of pricing models that allow quantitative risk assessment and support informed management decisions becomes particularly important. The aim of the article is to explore the possibilities of applying the Garman – Kohlhagen model to assess the fair value and risks of hryvnia currency options embedded in debt instruments, taking into account the specifics of the Ukrainian financial market. Within the study, the evolution of option pricing theory was analyzed, from the classical Black – Scholes model to its adaptation for the currency market, which considers the presence of two risk-free interest rates. Particular attention is paid to the problems of applying the Garman – Kohlhagen model in economies with a high level of currency and interest rate risks. The methodological basis of the study is an analytical approach to evaluating the value of currency options using the Garman – Kohlhagen model, financial modeling methods, comparative analysis, and quantitative risk assessment. The practical testing of the model was conducted using the example of a currency call option embedded in domestic government bonds indexed to the U.S. dollar – hryvnia currency pair, which serves as the underlying asset. Generalized market data on the hryvnia to U.S. dollar exchange rate, historical exchange rate volatility, as well as the zero-coupon yield curve for both the hryvnia and the U.S. dollar, were used for calculations. Market risk assessment was carried out based on the analysis of the option sensitivity parameters («Greeks»), which allows determining the impact of changes in key market factors on its fair value. As a result of the study, the economic feasibility of using the Garman – Kohlhagen model for valuing hryvnia-denominated currency options in the conditions of the Ukrainian financial market was substantiated. The obtained results confirm that taking into account interest rate differentials and exchange rate volatility allows for a more adequate valuation of the fair value of embedded currency derivatives and the associated risks. The practical significance of the results lies in the possibility of their use by banks and other financial institutions to improve the system of market risk management and to develop efficient hedging strategies. At the same time, the limitations of the model, related to the assumption of constant volatility and interest rates, have been identified, which opens up prospects for further research in the direction of using more complex models for pricing currency options. Prospects for further research lie in the application of models with stochastic volatility (in particular, the Heston model) and local volatility to increase the accuracy of valuing hryvnia-denominated currency derivatives under conditions of structural changes in the financial market of Ukraine. Expanding the methodological basis will allow for more accurately accounting for the effects of «heavy tails» and distribution asymmetry of exchange rate changes, characteristic of emerging markets.

Keywords: currency option; Garman – Kohlhagen model; currency risk; fair value; volatility; hedging; government bonds.

Fig.: 3. Tabl.: 1. Formulae: 7. Bibl.: 11.

Yakubets Andrii O. – Postgraduate Student, Department of Finance, National University of Kyiv-Mohyla Academy (2 Skovorody Str., Kyiv, 04655, Ukraine)
Email: [email protected]
Lukianenko Iryna H. – Doctor of Sciences (Economics), Professor, Professor, Department of Finance, National University of Kyiv-Mohyla Academy (2 Skovorody Str., Kyiv, 04655, Ukraine)
Email: [email protected]

List of references in article

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