# The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes

## Abstract

**:**

## 1. Introduction

## 2. Exchange Option

## 3. The Fractional Step Method

## 4. The Radial Basis Functions

## 5. Numerical Experiments

#### 5.1. General Setting

#### 5.2. Number of Partitions of Space Dimension

#### 5.3. Errors with Respect to Correlation

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | Several studies employ the ADI finite difference method to evaluate PDEs with mixed derivatives (Hendricks et al. 2016; In’t Hout and Foulon 2010; Jeong and Kim 2013). |

**Figure 1.**Pricing errors (in decimals) with respect to the number of partitions of space dimensions for $\rho =-0.75$ (

**Left**) and $\rho =0.75$ (

**Right**), respectively.

**Figure 2.**Pricing errors (in percentages) with respect to the number of partitions of space dimensions for $\rho =-0.75$ (

**Left**) and $\rho =0.75$ (

**Right**), respectively.

**Figure 3.**Computation time (in seconds) with respect to the number of partitions of space dimensions for the fractional step method (FS) (

**Left**) and the radial basis functions (RBF) (

**Right**).

**Figure 5.**Decimal (

**Left**) and percentage (

**Right**) pricing errors of the fractional step method (FS) and the radial basis functions (RBF) with respect to the correlation.

**Figure 6.**Percentage pricing errors of the fractional step method (FS) with a finer mesh, N = 120 and M = 250 with respect to the strong correlation.

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**MDPI and ACS Style**

Kagraoka, Y.
The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes. *Int. J. Financial Stud.* **2020**, *8*, 77.
https://doi.org/10.3390/ijfs8040077

**AMA Style**

Kagraoka Y.
The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes. *International Journal of Financial Studies*. 2020; 8(4):77.
https://doi.org/10.3390/ijfs8040077

**Chicago/Turabian Style**

Kagraoka, Yusho.
2020. "The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes" *International Journal of Financial Studies* 8, no. 4: 77.
https://doi.org/10.3390/ijfs8040077