Autori: Fusai, Gianluca , Atkinson, Colin
Titolo: The discrete extrema of the Brownian Motion and pricing of lookback options.
Periodico: Università degli Studi del Piemonte Orientale 'A. Avogadro' : Facoltà di Economia - Dipartimento di Scienze Economiche e Metodi Quantitativi "SEMEQ" - Quaderni
Anno: 2004 - Volume: 04 - Fascicolo: 86 - Pagina iniziale: 1 - Pagina finale: 28

In the present paper we provide a closed form expression for the distribution of the extrema of a Brownian motion observed at discrete times. We reduce the evaluation problem to a Wiener-Hopf equation that we solve analytically. We discuss the relationship of our result with the well known Spitzer identity. Finally we apply the result to the analytical evaluation of discrete lookback options in the Black-Scholes setting. The results from our analytical formulae are compared with those from other numerical methods available in the literature.


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