The British Lookback Option with Fixed Strike

Yerkin Kitapbayev

Applied Mathematical Finance, 2015, vol. 22, issue 3, 238-260

Abstract: We continue research of the new type of options called 'British' that was introduced recently by presenting the British lookback option with fixed strike. This article generalizes the work about the British Russian option and provides financial analysis of lookback options with fixed non-zero strike. The British holder enjoys the early exercise feature of American options whereupon his pay-off (deliverable immediately) is the 'best prediction' of the European lookback pay-off under the hypothesis that the true drift of the stock price equals a contract drift. We derive a closed-form expression for the arbitrage-free price in terms of the optimal stopping boundary of two-dimensional optimal stopping problem with a scaling strike and show that the rational exercise boundary of the option can be characterized via the unique solution to a nonlinear integral equation. We also show the remarkable numerical example where the rational exercise boundary exhibits a discontinuity. Using these results, we perform a financial analysis of the British lookback option with fixed strike, which shows that with the contract drift properly selected this instrument not only provides an effective protection mechanism, but becomes a very attractive alternative to the classic European/American lookback option from speculator's point of view and gives high returns when stock movements are favourable.

Date: 2015
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DOI: 10.1080/1350486X.2015.1019156

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