Estimation of parameters and valuation of options written on multiple assets described by uncertain fractional differential equations

Abstract

This study suggests the pricing problems of options dependent on multiple assets, spread, basket, and quanto options when the asset dynamics are described by the uncertain fractional differential equation. The solutions of these option prices are analytically provided and the algorithms related to each one of these derivatives are designed. For the first time, we apply the minimum cover method to estimate the parameters of the uncertain fractional differential equations based on the real data related to the stock prices of some markets. Through the uncertain hypothesis test, we demonstrate that the estimated uncertain fractional differential equations can successfully fit the observed data. We then experimentally show that the α-paths obtained by the estimated uncertain fractional differential equations favorably cover the sample data. Finally, some numerical experiments based on the uncertain fractional differential equation estimated by the minimum cover method are accomplished to confirm the achievement of the presented results.