Optimal Multiple Stopping Models of Reload Options and Shout Options

22 Pages Posted: 9 May 2005 Last revised: 12 Dec 2013

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Abstract

The reload provision in an employee stock option entitles its holder to receive one new (reload) option from the employer for each share tendered as payment of strike upon the exercise of the stock option. The number of reloads allowed can be finite or infinite. The shout feature in a call option allows its holder to reset the option's strike price to the prevailing stock price upon shouting. We explore symmetry relationship between the price functions of the employee reload options and shout call options. When the dividend yield of the underlying stock is zero, the value of the employee reload option can be expressed in terms of the price functions of a shout call option and forward contract. For an employee reload option with an infinite number of allowable reloads, the payoff of the employee reload option can be related to the lookback feature of the stock price process. We also examine the optimal exercise policies of the multi-reload employee stock options. The behaviors of the critical stock price at which the holder should exercise optimally are shown to depend on the relative magnitude of the dividend yield, interest rate and volatility. Our analysis of multi-reload and multi-shout options contributes to the literature on optimal stopping policies of contingent claims with multiple stopping rights.

Keywords: employee stock options, reload feature, shout call, multiple optimal stopping, lookback options

JEL Classification: G13

Suggested Citation

Dai, Min and Kwok, Yue Kuen, Optimal Multiple Stopping Models of Reload Options and Shout Options. Available at SSRN: https://ssrn.com/abstract=717382 or http://dx.doi.org/10.2139/ssrn.717382

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

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