Knock-In American Options

Journal of Futures Markets, Vol. 24, No. 2, pp. 179-192, 2004

12 Pages Posted: 12 Jan 2010 Last revised: 25 Jun 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

A knock-in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying asset price breaching certain trigger level (or called barrier level). We present closed form valuation formulas for knock-in American options under the Black-Scholes pricing framework. The price formulas possess different analytic representations, depending on the relation between the trigger stock price level and the critical stock price of the underlying American option. We also performed numerical valuation of several knock-in American options to illustrate the efficacy of the price formulas.

Keywords: Barrier options, American options, knock in, analytic solutions

JEL Classification: G130

Suggested Citation

Dai, Min and Kwok, Yue Kuen, Knock-In American Options. Journal of Futures Markets, Vol. 24, No. 2, pp. 179-192, 2004. Available at SSRN: https://ssrn.com/abstract=669502

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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