Distance to the line in the Heston model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:450

Article

Gulisashvili, Archil¹ 

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

关键词: Heston manifold;    Distance to the line;    Level sets;    Minimization problems;    Implied volatility;   

DOI  :  10.1016/j.jmaa.2017.01.014

来源: Elsevier

【 摘 要 】

The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimisation problems for functions of one variable over finite intervals. One of the main ideas in this paper is to use a new system of coordinates in the Heston manifold and the level sets associated with this system. In the case of a verticanine, the formulas for the distance to the line are rather simple. For slanted lines, the formulas are more complicated, and a more subtle analysis of the level sets intersecting the given line is needed. We also find simple formulas for the Heston distance from a point to a level set. As a natural application, we use the formulas obtained in the present paper in the study of the small maturity limit of the implied volatility in the Heston model. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free