THE BRITISH KNOCK-OUT PUT OPTION

Luluwah Al-Fagih ()
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Luluwah Al-Fagih: School of Mathematics, Kingston University London, KT1 2EE, United Kingdom;

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 02, 1-32

Abstract: Following the economic rationale introduced by Peskir & Samee (2011, 2013) we present a new class of barrier options within the British payoff mechanism where the holder enjoys the early exercise feature of American type options whereupon his payoff (deliverable immediately) is the best prediction of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Should the option holder believe the true drift of the stock price to be unfavorable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. In this paper, we focus on the knock-out put option with an up barrier. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results, we perform a financial analysis of the British knock-out put option. We spot some of the trends previously seen in Peskir & Samee (2011) but observe some behavior unique to the knock-out case. Finally, we derive the British put-call and up-down symmetry relations which express the arbitrage-free price and the rational exercise boundary of the British down-and-out call option in terms of the arbitrage-free price and the rational exercise boundary of the British up-and-out put option.

Keywords: British option; European/American barrier option; knock-out option; stopped process; arbitrage-free price; British barrier put-call symmetry; liquid/illiquid market; free-boundary problem; nonlinear integral equation; local time-space calculus (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024915500089

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