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Nice notes by Yue-Kuen KWOK
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Fabio Mercurio
Financial Models, Banca IMI

-Notes and formula
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Min Dai
Hoi Ying Wong
Yue Kuen Kwoky
Abstract. The lookback feature in a quanto option refers to the payo structure where the terminal payo of the quanto option depends on the realized extreme value of either the stock price or the exchange rate. In this paper, we study the pricing models of European and American lookback option with the quanto feature. The analytic price formulas for two types of European style quanto lookback options are derived. The success of the analytic tractability of these quanto lookback options depends on the availability of a succinct analytic representation of the joint density function of the extreme value and terminal value of the stock price and exchange rate. We also analyze the early exercise policies and pricing behaviors of the quanto lookback option with the American feature. The early exercise boundaries of these American quanto lookback options exhibit properties that are distinctive from other two-state American option models.

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