PRICING PARISIAN-STYLE OPTIONS WITH A LATTICE METHOD

Marco Avellaneda and Lixin Wu
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Marco Avellaneda: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, USA and Morgan Stanley, New York, USA
Lixin Wu: Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong, China

International Journal of Theoretical and Applied Finance (IJTAF), 1999, vol. 02, issue 01, 1-16

Abstract: A Parisian-style barrier option expires if the price of the underlying asset remains above or below some level(s) continuously over a specified period of time (the "window"). A trinomial-lattice scheme is developed for calculating the price and the sensitivities of such options. Monte–Carlo simulation of hedging events using the resulting deltas show errors which are of the same magnitude as for hedging vanilla options, confirming the validity of proposed scheme. We use these results to price callable and convertible bonds with this "window" feature.

Date: 1999
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DOI: 10.1142/S0219024999000029

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