An algorithm to determine the parameters of S_U-curves in the johnson system of probabillity distributions by moment matching ^∗

^∗This paper was written while the author was a visiting scholar in the Finance Area at the Schulich School of Business. I would like to thank Dr. Moshe Milevsky, who introduced me to the problem and acted as a sponsor for the duration of my visit. Furthermore, I would like to thank Dr. Chris Robinson, who very kindly made his office available as a working space during this period.

Abstract

We describe an algorithm to fit an S_U -Curve of the Johnson system by moment matching. The algorithm follows from a new parametrization, and reduces the problem to a root finding procedure that can be implemented efficiently using a bisection or a Newton-Raphson method. This allows the four parameters of the Johnson curve to be determined to any desired degree of accuracy, and is fast enough to be implemented in a real-time setting. A practical application of the method lies in the fact that many firms use the Johnson system to manage financial risk

Keywords:

• Johnson System
• Moment Matching
• Option Pricing

^∗This paper was written while the author was a visiting scholar in the Finance Area at the Schulich School of Business. I would like to thank Dr. Moshe Milevsky, who introduced me to the problem and acted as a sponsor for the duration of my visit. Furthermore, I would like to thank Dr. Chris Robinson, who very kindly made his office available as a working space during this period.

^∗This paper was written while the author was a visiting scholar in the Finance Area at the Schulich School of Business. I would like to thank Dr. Moshe Milevsky, who introduced me to the problem and acted as a sponsor for the duration of my visit. Furthermore, I would like to thank Dr. Chris Robinson, who very kindly made his office available as a working space during this period.

Notes

^∗This paper was written while the author was a visiting scholar in the Finance Area at the Schulich School of Business. I would like to thank Dr. Moshe Milevsky, who introduced me to the problem and acted as a sponsor for the duration of my visit. Furthermore, I would like to thank Dr. Chris Robinson, who very kindly made his office available as a working space during this period.