Long-Term and Blow-Up Behaviors of Exponential Moments in Multi-Dimensional Affine Diffusions

Stochastic Processes and their Applications, vol. 122, 2961-2993

Posted: 30 Dec 2013

See all articles by Rudra Jena

Rudra Jena

Independent

Kyoung-Kuk Kim

Korea Advanced Institute of Science and Technology

Hao Xing

Boston University - Questrom School of Business

Date Written: May 23, 2012

Abstract

This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where log-returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.

Keywords: Affine diffusions; Exponential moments; Riccati differential equations; Implied volatility

Suggested Citation

Jena, Rudra and Kim, Kyoung-Kuk and Xing, Hao, Long-Term and Blow-Up Behaviors of Exponential Moments in Multi-Dimensional Affine Diffusions (May 23, 2012). Stochastic Processes and their Applications, vol. 122, 2961-2993, Available at SSRN: https://ssrn.com/abstract=2372825

Rudra Jena

Independent ( email )

No Address Available
United States

Kyoung-Kuk Kim (Contact Author)

Korea Advanced Institute of Science and Technology ( email )

Dept of Industrial and Systems Engineering
KAIST
Daejeon, 305-701
Korea, Republic of (South Korea)

Hao Xing

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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