Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs

Figures & data

Figure 1. Comparison of the spot exchange rate’ sample paths in the $\mathit{F}\mathit{B}\mathit{S}$ model (left) and the subdiffusive $\mathit{F}\mathit{B}\mathit{S}$ model (right) for ${\mathit{r}}_{\mathit{d}}\mathbf{=}\mathbf{0.03},{\mathit{r}}_{\mathit{f}}=\mathbf{0.02}\mathbf{,}$ $\mathit{\alpha }\mathbf{=}\mathbf{0.9}\mathbf{,}\mathbf{H}\mathbf{=}\mathbf{0.8},\mathit{\sigma }\mathbf{=}\mathbf{0.1},{\mathit{S}}_{\mathbf{0}}\mathbf{=}\mathbf{1}$.

Figure 2. Call currency option values.

Figure 3. Relative difference between the $\mathit{G}\mathbf{-}\mathit{K}$, $\mathit{F}\mathit{B}\mathit{S}$, and subdiffusive $\mathit{F}\mathit{B}\mathit{S}$ models for the in-the-money case.

Figure 4. Relative difference between the $\mathit{G}\mathbf{-}\mathit{K}$, $\mathit{F}\mathit{B}\mathit{S}$, and subdiffusive $\mathit{F}\mathit{B}\mathit{S}$ models for the out-of-the-money case.