Autore
Fusai, Gianluca

Titolo
THE WIENER-HOPF TECHNIQUE & DISCRETELY MONITORED PATH DEPENDENT OPTION PRICING
Periodico
Università degli Studi del Piemonte Orientale 'A. Avogadro' : Facoltà di Economia - Dipartimento di Scienze Economiche e Metodi Quantitativi "SEMEQ" - Quaderni
Anno: 2008 - Fascicolo: 8 - Pagina iniziale: 1 - Pagina finale: 32

Fusai et al. (2006) employed the Wiener-Hopf technique to obtain an exact analytic expression for discretely monitored barrier option prices as the solution to the Black-Scholes partial differential equation (PDE). The present work reformulates this in the language of random walks and extends it to price a variety of other discretely monitored path dependent options. Analytic arguments familiar in the applied mathematics literature are used to obtain fluctuation identities. This includes casting the famous identities of Baxter and Spitzer in a form convenient to price barrier, first-touch and hindsight options. Analyzing random walks killed by two absorbing barriers with a modified Wiener-Hopf technique yields a novel formula for double-barrier option prices. Continuum limits and continuity correction approximations are considered. Numerically efficient results are obtained by implementing Pad´e approximation. A Gaussian Black-Scholes framework is used as a simple model to exemplify the techniques, but the analysis applies to L´evy processes generally.



Testo completo: http://semeq.unipmn.it/files/quaderno%20completo%20n.8%20fusai.pdf

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