A Continuous-Exercise Model for American Call Options with Hedging Constraints

19 Pages Posted: 4 Apr 2016 Last revised: 16 Apr 2016

See all articles by Cong Qin

Cong Qin

Center for Financial Engineering

Xinfu Chen

Independent

Xin Lai

College of Science

Wanghui Yu

Soochow University

Date Written: September 1, 2015

Abstract

In this paper, we derive a parabolic variational inequality with double time-like variables from a continuous exercise model of American call options proposed in Rogers and Schienkman (2007). Using viscosity approach, we prove that the value function is a unique viscosity solution to the variational inequality. For the perpetual problem, we first obtain some conditions which guarantee the problem is well posed.

Then, under exponential utility, we explicitly construct the optimal exercise strategy based on the free boundary of the variational inequality. Finally, with the closed-form solutions in two cases that zero interest rate and zero strike price, we prove that the optimal exercise price in one-time exercise model is no smaller than the starting exercise price in the continuous exercise model.

Keywords: American call options, continuous exercise, variational inequality, optimal exercise strategy, free boundary

Suggested Citation

Qin, Cong and Chen, Xinfu and Lai, Xin and Yu, Wanghui, A Continuous-Exercise Model for American Call Options with Hedging Constraints (September 1, 2015). Available at SSRN: https://ssrn.com/abstract=2757541 or http://dx.doi.org/10.2139/ssrn.2757541

Cong Qin (Contact Author)

Center for Financial Engineering ( email )

No. 1 Shizi Street, Center for Financial Engineeri
Suzhou, 215006
China
13656190706 (Phone)

Xinfu Chen

Independent ( email )

No Address Available
United States

Xin Lai

College of Science ( email )

Tianjin, 300300
China

Wanghui Yu

Soochow University ( email )

No. 1 Shizi Street
Taipei, Jiangsu 215006
Taiwan

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