Search Results (3)

Uncertain fractional differential equations (UFDEs) are excellent tools for describing complicated dynamic systems. This study analyzes the valuation problems of currency options based on UFDE under the optimistic value criterion. Firstly, a new uncertain fractional currency model is formulated to describe the dynamics of the foreign exchange rate. Then, the pricing formulae of European, American, and Asian currency options are obtained under the optimistic value criterion. Numerical simulations are performed to discuss the properties of the option prices with respect to some parameters. Finally, a real-world example is provided to show that the uncertain fractional currency model is superior to the classical stochastic model. Full article

Technological innovation has changed the financial market significantly with the increasing application of high-frequency data in research and practice. This study examines the performance of intraday implied volatility (IV) in estimating currency options prices. Options quotations at a different trading time, such as the opening period, midday period and closing period of a trading day with one-month, two months’ and three months’ maturity, are employed to compute intraday IV for pricing currency options. We use the Mincer–Zarnowitz regression test to analyse the volatility forecast power of IV for three different forecast horizons (within a week, one week and one month). Intraday IV’s capability in estimating currency options price is measured by the mean squared error, mean absolute error and mean absolute percentage error measure. The empirical findings show that intraday IV is the key to accurately forecasting volatility and estimating currency options prices precisely. Moreover, IV at the closing period of the beginning of the week contains crucial information for options price estimation. Furthermore, the shorter maturity intraday IV is suitable for pricing options for a shorter horizon. In comparison, the intraday IV based on the longer maturity options subsumes appropriate information to price options with higher accuracy for the longer horizon. Our paper proposes a new approach to accurately pricing currency options using high-frequency data. Full article

The foreign exchange market comprises the largest global volume, so the pricing of foreign exchange options has always been a hot issue in the foreign exchange market. This paper treats the exchange rate as an uncertain process that is described by an uncertain fractional differential equation, and establishes a new uncertain fractional currency model. The uncertain process is driven by Liu process, and, with the application of the Mittag-Leffler function, the solution of the fractional differential equation in a Caputo sense is presented. Then, according to the uncertain fractional currency model, the pricing formulas of European and American currency options are given. Lastly, the two numerical examples of European and American currency options are given; the price of the currency option increased when p changed from 1.0 to 1.1, and prices with different p were all decreasing functions of exercise price K. Full article