Some Integral Functionals of Reflected Sdes and Their Applications in Finance

Quantitative Finance, 11(3): 343--348, March 2011.

10 Pages Posted: 15 Jun 2011 Last revised: 14 Jun 2017

See all articles by Xuewei Yang

Xuewei Yang

Nanjing University - School of Management and Engineering; Nanjing University - Institute of New Finance

Lijun Bo

University of Science and Technology of China (USTC)

Yongjin Wang

Nankai University - Business School

Date Written: June 14, 2008

Abstract

In this paper, we consider a class of reflected stochastic differential equations (abbr. SDEs) and we are particularly interested in some integral functionals of the solutions to the equations. We explicitly derive the Laplace transforms of those integral functionals, which are subsequently applied for the financial arguments. Here we consider a regulated market, in which the price dynamics is driven by a reflected SDE. We will calculate the conditional default probability under such price dynamics, and meanwhile we also give the pricing on some digital options. Finally, for practical purpose, an illustration for the numerical inversion of the Laplace transforms is presented in the Appendix.

Keywords: Reflected stochastic differential equation, integral functionals, Laplace transform, numerical inversion, conditional default probability, digital option

JEL Classification: G12

Suggested Citation

Yang, Xuewei and Bo, Lijun and Wang, Yongjin, Some Integral Functionals of Reflected Sdes and Their Applications in Finance (June 14, 2008). Quantitative Finance, 11(3): 343--348, March 2011., Available at SSRN: https://ssrn.com/abstract=1864690

Xuewei Yang (Contact Author)

Nanjing University - School of Management and Engineering ( email )

22 Hankou Road, Gulou District
Nanjing, Jiangsu 210093
China

Nanjing University - Institute of New Finance ( email )

Nanjing, Jiangsu 210093
China

Lijun Bo

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Yongjin Wang

Nankai University - Business School ( email )

94 Weijin Road, Nankai District
Tianjin, 300071
China

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