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

Posedel, Petra

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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

Petra Posedel, University of Zagreb, Faculty of Economics and Business, Zagreb, Croatia

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.

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

Year: 2006 | Volume: 30 | Issue: 4 | Pages: 347 - 368

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