HYBRID MODEL FOR VALUATION OF OPTIONS EMBEDDED IN INDEXED GOVERNMENT BONDS

Abstract

The article describes the payoff calculation for options embedded in Ukrainian government bonds indexed to USD/UAH rate. It also outlines characteristics of embedded options that make their valuation a complicated task. Namely, that USD/UAH averaging takes place only in the last month of option’s life. Common market and regulatory practice for valuation of embedded options in Ukraine, which implies additional assumptions to standard Garman-Kohlhagen model, is presented. The need for development of new model is justified. The new model should specifically take into account the non-standard payoff of embedded option, which uses arithmetic averaging only in the last month of option’s life. Key features of Hull-White approach for valuation of Asian options are described, including the formula for calculating indicative average prices. Article proceeds to separate embedded option’s life into two key parts. The first part includes time, from where USD/UAH rate is not included in option’s payoff formula (period without averaging). The second part includes time from where embedded option becomes a pure Asian option, as all USD/UAH rates from this period are included in option’s payoff formula (period with averaging). The latter part causes the path-dependance of embedded option’s value. The new model for valuation of embedded option is developed. The new model is a hybrid of standard binomial tree model and Hull-White model, where the former is used in the first period of option’s life (period without averaging), and the latter is used in the second period where averaging takes place. Three sample options with different maturities, issue dates and other inputs are valued using the hybrid model. Valuation results are compared to the model used by banks’ regulator and Monte Carlo benchmark. It is concluded that hybrid model’s valuations are considerably closer to Monte Carlo benchmark results than its counterpart’s. Hybrid model is tested for its sensitivity to arbitrary parameter h. It is discovered that the model has a low sensitivity to parameter h. Thus, model risk related to arbitrary parameter is not material.